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HOME  UNIVERSITY  LIBRARY 
OF  MODERN  KNOWLEDGE 

No.  53 


Editon: 

HERBERT    FISHER,  M.A.,  F.B.A. 
PROF.    GILBERT    MURRAY,    LiTT.D., 

LL.D.,  F.B.A. 

PROF.  J.  ARTHUR    THOMSON,  M.A. 
PPOF.  WILLIAM   T.  BREWSTER,  M.A. 


A  complete  classified  list  of  tht  volumes  of  THE 
HOME  UNIVERSITY  LIBRARY  already  published 
will  be  found  at  the  back  of  this  book. 


ELECTRICITY 


BY 

GISBERT  KAPP 

PROFESSOR  OF  ELECTRICAL  ENGINEERING  AT  THE 
UNIVERSITY,  BIRMINGHAM 


NEW   YORK 
HENRY   HOLT  AND   COMPANY 

LONDON 
WILLIAMS   AND   NORGATE 


CONTENTS 

CHAP.  PAOB 

I      ON   FORCES  ACTING  THROUGH  SPACE             .  7 

II      ON  PRICTIONAL  AND  CONTACT  ELECTRICITY  34 

III  ON   POTENTIAL  .  .  .  .  .55 

IV  ELECTRIFICATION   BY   MECHANICAL   MEANS.  87 
V      THE   ELECTRIC   CURRENT    .            .            .            .113 

VI      THK   DYNAMICS   OF   ELECTRIC   CURRENTS      .  141 

VII      THE    DYNAMIC    GENERATION    OF     ELECTRIC 

CURRENTS 170 

VIII      ALTERNATING   CURRENTS    ....  203 

IX      THE   DISTRIBUTION   OF   ELECTRICITY               .  228 

BIBLIOGRAPHY 253 

INDEX 255 


!;s. 


ELECTRICITY 

CHAPTER  I 

ON   FORCES   ACTING   THROUGH   SPACE 

THE  conception  of  a  force  as  something 
which  pushes  or  pulls  is  familiar  to  every 
one.  Equally  familiar  is  the  conception  of 
an  intervening  link  by  which  a  force  is  trans- 
mitted from  one  body  to  another.  If  I  pull 
a  bucket  of  water  out  of  a  well  the  push 
exerted  by  the  water  on  the  bottom  of  the 
pail  is  transmitted  to  my  hand  by  a  very 
simple  series  of  links.  The  bottom  of  the 
bucket  pulls  at  its  sides,  these  pull  at  the 
handle,  the  handle  pulls  the  rope,  and  that 
finally  pulls  at  my  hand.  We  have  here  a 
transmission  of  force  by  links,  all  of  which 
are  in  bodily  contact.  Thus  far  the  process 
of  transmission  presents  no  difficulty  to  our 
conception  of  a  force,  but  when  we  come  to 
inquire  why  the  water  presses  against  the 

7 


S  ELECTRICITY 

bottom  of  the  bucket,  we  have  no  complete 
answer.  All  we  can  say  is  that  the  push  is 
due  to  the  fact  that  the  water  is  heavy.  This 
means  that  the  water  in  our  bucket  is  attracted 
towards  the  earth,  but  what  kind  of  inter- 
vening link  there  is  which  transmits  a  force 
from  the  earth  to  every  particle  of  water  and 
every  particle  of  bucket  and  rope  we  are  quite 
unable  to  say.  Everyday  experience  has  so 
familiarised  us  with  the  action  of  gravity  that 
we  have  become  accustomed  to  simply  accept- 
ing it  as  a  fact  in  nature,  without  further 
inquiry  as  to  the  machinery  which  is  instru- 
mental in  the  transmission  of  this  force 
through  the  intervening  space.  We  simply 
say  that  gravity  is  a  force  that  acts  at  a 
distance,  and  since  by  direct  experiment  and 
astronomical  observation  it  has  been  found  pos- 
sible to  formulate  a  mathematical  expression 
for  this  force,  there  is,  from  a  purely  practical 
point  of  view,  no  need  to  find  an  explana- 
tion of  the  machinery  by  which  this  force  is 
transmitted  through  space,  whether  the  space 
be  quite  empty  or  filled  with  other  bodies. 

The  confession  of  ignorance  as  to  the 
nature  of  this  machinery  of  transmission  is, 
however,  not  a  denial  that  such  machinery 
exists;  on  the  contrary,  the  conception  that 


ACTION  OF  FORCES  9 

physical  action  can  take  place  without  the 
intervention  of  physical  causes  is  repugnant 
to  the  human  mind,  and  therefore  physicists 
have  invented  the  ether.  By  this  they  mean 
a  physical  something  which  pervades  all 
space,  whether  filled  by  bodies  or  not,  and 
this  ether  forms  the  connecting  link  by  which 
forces  are  transmitted  across  space.  Once 
we  assume  the  existence  of  this  physical 
though  imponderable,  that  is,  weightless 
substance,  we  may  regard  it  as  instrumental 
not  only  in  the  transmission  of  gravitational 
forces,  but  also  of  electric  and  magnetic  forces 
and  as  the  carrier  of  light  and  heat  rays. 
There  is,  indeed,  very  strong  experimental 
evidence  that  light,  electricity,  magnetism 
and  all  other  manifestations  of  energy  are 
propagated  by  ether  vibrations.  Maxwell 
was  the  first  to  point  out  that  a  connec- 
tion of  this  kind  exists,  and  by  adopting 
his  "  electromagnetic  theory  of  light "  it 
can  be  proved  mathematically,  what  has  also 
been  experimentally  verified,  that  the  speed 
at  which  a  telegraph  signal  travels  along  the 
wire  is  equal  to  the  speed  of  light  propagation. 
It  is  extremely  unlikely  that  such  an  agree- 
ment should  be  a  mere  coincidence,  and  we 
are  therefore  justified  in  assuming  that  the 


10  ELECTRICITY 

ether,  although  originally  invented  to  bridge 
a  gap  in  our  reasoning,  has  nevertheless  a  real 
existence. 

The  acceptance  of  the  ether  as  the  medium 
of  propagation  of  all  kinds  of  forces  across 
space  does  not  explain  the  mechanism  of  its 
action,  but,  by  ascribing  to  the  ether  certain 
properties,  we  are  able  to  express  in  concrete 
figures,  by  the  use  of  any  convenient  system 
of  measurement,  the  results  of  experimental 
investigation.  The  general  law  of  action  at 
a  distance  has  been  proved  by  direct  experi- 
ment and  by  astronomical  observation  to  be 
as  follows  :  Let  two  active  masses  be  con- 
centrated in  two  points  a  certain  distance 
apart;  then  the  force  acting  between  them, 
that  is,  the  force  which  is  being  transmitted 
from  one  point  to  the  other  by  the  inter- 
vention of  the  ether,  is  proportional  to  the 
product  of  the  two  masses  and  inversely  pro- 
portional to  the  square  of  their  distance.  In 
the  case  of  gravity  this  force  is  always  at- 
tractive, that  is,  tending  to  bring  the  masses 
nearer  together;  in  the  case  of  electricity  or 
magnetism  it  may  be  attractive  or  repulsive 
according  to  the  nature  of  the  active  masses. 

It  should  be  noted  that  the  term  "  active 
mass "  is  merely  conventional  as  far  as 


ACTION  OF  FORCES  11 

electricity  or  magnetism  is  concerned.  It  is 
not  to  be  taken  in  its  literal  sense  as  applying 
to  something  which  has  bulk  and  weight.  A 
steel  bar,  after  being  magnetised,  weighs 
exactly  the  same  as  before,  yet  its  ends  exhibit 
certain  properties  which  we  may  convention- 
ally ascribe  to  accumulations  of  magnetic 
matter  which,  if  brought  near  magnetic 
matter  adhering  to  the  end  of  some  other 
magnetised  bar,  becomes  "  active  matter " 
in  the  sense  of  producing  either  attraction  or 
repulsion.  The  force  is  attractive  if  the  ends 
of  the  bars  brought  near  each  other  contain 
magnetic  matter  of  opposite  sign,  and  it  is 
repulsive  if  the  magnetism  is  of  the  same  sign. 
In  the  same  way  there  is  repulsion  between 
two  conductors  both  positively  or  both  nega- 
tively electrified,  and  there  is  attraction  if 
one  is  positively  and  the  other  negatively 
electrified.  Also  in  this  case  electrification 
does  not  alter  the  weight  of  the  conductor, 
although  we  may  consider  the  electricity  car- 
ried by  the  conductor  as  an  "  active  mass  " 
in  the  sense  that  the  force  of  attraction  or 
repulsion  acting  through  space  is  due  to  it. 
In  gravitation  the  force  is  always  attractive, 
whilst  with  magnetism  or  electricity  as  active 
matter  the  force  may  be  either  attractive  or 


12  ELECTRICITY 

repulsive;  in  all  cases,  however,  the  same 
law  applies  as  to  the  action  through  space. 
The  reader  should  note  that  the  above 
statement  of  this  law  is  no  complete  answer 
to  the  question  as  to  the  actual  magnitude  of 
the  force.  Experiment  only  teaches  us  that 
the  force  is  proportional  to  the  product  of  the 
two  masses  divided  by  the  square  of  their 
distance,  but  if  we  wish  to  state  the  actual 
magnitude  of  this  force  in  a  definite  figure  we 
must  agree  on  a  system  of  units.  As  far  as 
the  attractive  force  between  ponderable 
masses  is  concerned,  such  units  are  quite 
familiar;  we  know  what  is  meant  by  the 
mass  of  a  pound  weight,  and  we  also  know 
how  to  measure  a  distance.  With  magnetic 
and  electric  forces  the  matter  is  not  so  simple. 
A  distance  we  can  measure  in  any  length  unit, 
but  what  about  the  unit  for  the  "  active 
mass  "  ?  We  have  seen  that  it  is  not  a  mass 
at  all  in  the  common  acceptance  of  this  term, 
and  it  can  therefore  not  be  expressed  in  any 
unit  suitable  for  ponderable  masses.  We  are 
thus  compelled  to  settle  the  magnitude  of 
the  unit  by  the  same  formula  which  defines 
the  force.  The  conception  of  unit  active  mass 
may  then  be  derived  from  the  following  con- 
dition: If  two  equal  masses  one  centimetre 


ACTION  OF  FORCES  13 

apart  act  upon  each  other  with  unit  force, 
then  each  of  them  is  a  unit  of  active  mass. 

The  same  definition  of  unit  mass  must  also 
fit  if  applied  to  gravitational  attraction,  but 
there  is  a  difference.  We  know  from  experi- 
mental evidence  (T.  Erismann,  Arch.  d. 
Science,  Jan.  1911,  pp.  36-45)  that  the  at- 
tractive force  of  gravity  is  not  in  the  least 
influenced  by  the  medium  which  fills  the  inter- 
vening space.  Two  bodies  in  air  attract  each 
other  with  exactly  the  same  force  as  in  water ; 
nor  would  the  force  be  altered  if  we  placed  a 
wall  between  them.  There  would  of  course  be 
an  additional  attraction  between  each  body 
and  the  wall,  but  no  additional  force  of  the 
attraction  between  the  bodies  themselves. 

With  magnetic  and  electric  forces  it  is 
different.  If  the  force  acting  between  two 
electrically  charged  bodies  be  measured, 
first  in  air  and  then  when  immersed  in 
oil  or  separated  by  a  wall  of  glass,  we 
should  find  a  decrease  of  force  in  the  latter 
cases.  In  these  cases  the  whole  or  part  of 
the  medium  which  at  first  was  air  has  been 
replaced  by  some  other  substance  with  the 
result  of  an  alteration  in  the  force.  We 
thus  find  that  not  only  the  magnitude  of  the 
charges  and  their  distance,  but  also  the 


14  ELECTRICITY 

physical  nature  of  the  intervening  medium 
has  an  influence  on  the  force,  and  the  mathe- 
matical formula  expressing  the  magnitude  of 
the  force  must  take  account  of  this.  We 
must  therefore  introduce  into  the  formula  a 
coefficient,  the  numerical  value  of  which  will 
not  only  depend  on  the  system  of  units  chosen, 
but  also  on  the  medium  filling  the  space 
through  which  the  force  acts.  We  thus 
arrive  at  the  following  mathematical  ex- 
pression— 

F_  .Mm 
"'  D2 

where  M  and  m  are  the  two  masses,  D  is  the 
distance  and  F  is  the  force,  all  expressed  in  any 
system  of  units  which  may  be  convenient  for 
the  particular  case  in  hand.  The  coefficient 
/  will  naturally  depend  on  the  magnitude  of 
the  units  chosen;  on  their  nature,  that  is, 
whether  we  deal  with  gravitational  masses,  elec- 
tric charges  or  magnetism ;  and  on  the  medium 
filling  the  space  through  which  the  force  acts. 

We  do  not  know  what  electricity  is  any 
more  than  we  know  what  magnetism  is; 
all  we  know  is  that  they  are  not  of  the 
nature  of  ponderable  masses,  and  that  under 
certain  circumstances  they  may  become  the 
vehicle  for  the  transmission  of  energy  in  a 


ACTION  OF  FORCES  15 

similar  manner  to  the  ether  itself.  We  might, 
in  fact,  consider  them  as  ethereal  manifest- 
ations without  any  attempt  to  explain  the 
exact  nature  and  mechanism  of  these  mani- 
festations. Such  a  conception  is  quite  com- 
patible with  the  practical  use  of  our  general 
formula;  it  simply  means  that  we  must  look 
upon  /  as  a  kind  of  ethereal  coefficient,  the 
numerical  value  of  which  has  to  be  found 
experimentally. 

The  conception  of  an  ethereal  coefficient, 
stated  in  this  general  way,  is  perhaps  a  little 
difficult  to  grasp.  To  make  the  matter  clear 
I  start  by  applying  it  to  the  familiar  pheno- 
menon of  gravity,  and  then  proceed  to  in- 
vestigate the  more  unfamiliar  phenomena  of 
electric  and  magnetic  forces.  At  the  outset 
we  must  agree  on  the  units  we  are  going  to  use 
in  giving  a  numerical  expression  to  the 
attractive  force  between  two  bodies.  If  one 
of  these  bodies  is  the  earth  and  the  other  a 
stone,  this  force  is  simply  the  weight  of  the 
stone.  If  the  two  bodies  are  the  earth  and 
the  moon,  the  force  is  that  which  just  balances 
the  centrifugal  force  experienced  by  the  moon 
in  flying  round  in  her  orbit.  The  formula 
for  the  attraction  given  on  p.  14  refers  to 
masses  concentrated  in  points,  and  it  might 


16  ELECTRICITY 

thus  at  first  sight  appear  that  its  application 
to  such  a  bulky  object  as  our  earth  is  not 
permissible.  Neither  moon  nor  earth  can 
be  considered  infinitely  small  as  compared  to 
their  distance.  Nevertheless  we  may  use  the 
formula,  for  a  mathematical  investigation 
shows  that  in  the  case  of  spheres  the  summar- 
ised effects  of  all  mass  particles  is  the  same  as 
if  the  total  mass  were  concentrated  in  the 
centre.  Astronomy  gives  us  all  the  data 
required  for  our  calculation;  all  we  need  to 
get  a  definite  numerical  result  is  to  agree  on 
a  definite  system  of  units  in  which  to  express 
a  force. 

The  definition  of  a  mechanical  force  is :  some- 
thing which  produces  acceleration  of  a  ponder- 
able mass.  Acceleration  is  the  rate  at  which 
speed  increases  in  respect  of  time.  Thus,  if 
an  electric  tramcar  starting  from  rest  attains 
its  full  speed  of  24  miles  per  hour  in  the  time 
of  20  seconds,  its  average  acceleration  is  1-2 
miles  per  hour  in  each  succeeding  second,  or 
"  1-2  miles  per  hour  per  second."  If  instead 
of  giving  the  speed  in  miles  per  hour  we  give 
it  in  metres  per  second,  the  acceleration  of 
this  car  would  be  0-535  metres  per  second 
per  second.  Taking  the  metre  as  the  unit  of 
length,  the  second  as  the  unit  of  time,  and  the 


ACTION  OF  FORCES  17 

kilogram  as  the  unit  of  force,  we  have  thereby 
also  settled  what  the  unit  of  mass  must  be. 

A  stone  weighing  one  kilogram,  and  in 
fact  any  stone,  when  starting  to  fall  from 
rest,  acquires  in  the  first  second  a  velocity 
of  9-81  metres  per  second.  Its  acceleration 
or  gain  of  speed  is  therefore  9-81  metres  per 
second  per  second.  Since  the  force  which 
pulls  the  stone  towards  the  earth  is  one  kilo- 
gram, and  since  in  any  system  of  units  the 
product  of  mass  and  acceleration  represents 
force,  the  mass  of  our  stone  is  the  9- 81th  part 
of  unit  mass.  Therefore  in  the  particular 
system  of  units  chosen  in  this  example,  a 
stone  weighing  9-81  kilograms  has  unit  mass. 

Expressing  now  the  known  masses  of  earth 
and  moon  in  this  system,  and  remembering 
that  the  average  radius  of  the  moon's  orbit 
is  385,080  km.,  and  the  length  of  the  month 
27  days  7  hours  43  minutes,  it  is  easy  to 
calculate  the  centrifugal  force  from  the  well- 
known  relation  between  mass,  radius  and  time 
of  revolution.  The  result  is  in  round  numbers 
20,000  million  million  tons.  It  is  difficult  to 
grasp  the  meaning  of  so  prodigious  a  force, 
but  we  may  get  an  idea  of  its  magnitude  by 
calculating  the  diameter  of  a  cylindrical  bar 
of  the  strongest  steel  able  to  just  support  the 

B 


18  ELECTRICITY 

application  of  such  a  force  longitudinally. 
It  comes  out  at  320  miles  in  diameter.  Having 
thus  found  the  force,  we  can  now  determine 
the  numerical  value  of  the  ethereal  coefficient 
of  mass  attraction  for  the  particular  units 
chosen,  namely,  the  metre  as  the  unit  of  length, 
the  kilogram  as  the  unit  of  force,  and  a  mass 
of  9-81  kilogram  weight  as  the  unit  of  mass. 
The  result  of  this  calculation  is 

,  _  6-47 
=  1010 

The  symbol  1010  means  that  10  is  to  be  multi- 
plied 10  times  with  itself.  The  numerical  ex- 
pression for  /  may  also  be  written  in  the  form 

/  =  6-47  X  10-10 

where  the  minus  sign  of  the  exponent  signifies 
that  6-47  is  not  to  be  multiplied,  but  divided 
by  1010. 

In  the  above  example  showing  how  the 
ethereal  coefficient  may  be  determined  for 
any  arbitrary  system  of  units,  I  have  taken 
as  the  unit  of  mass  the  mass  of  9-81  kg. ;  this 
was  merely  done  as  a  matter  of  convenience, 
so  as  to  be  able  to  regard  the  kg.  as  the  unit 
of  force,  as  is  customary  in  engineering.  It 
is,  however,  more  in  consonance  with  first 
scientific  principles  not  to  fix  arbitrarily  a 


ACTION  OF  FORCES  19 

unit  for  the  force,  but  derive  it  from  the  three 
fundamental  units  of  mass,  length  and  time, 
since  every  physical  quantity  may  be  ex- 
pressed by  reference  to  these  three  units. 
If  we  choose  the  centimetre  as  the  unit  of 
length,  the  gram  as  the  unit  of  mass  and  the 
second  as  the  unit  of  time,  we  adopt  what 
physicists  call  the  centimetre  -  gram  -  second 
system  of  measurement.  For  this  the  abbre- 
viated designation  c.g.s.  is  customary.  In  this 
system  force  is  a  so-called  derived  unit, 
namely  that  force  which,  acting  steadily  in 
the  same  direction  for  a  second  on  the  mass 
of  one  gram,  will  give  it  an  acceleration  of 
one  cm.  per  second  per  second.  This  unit 
is  called  the  dyne,  and  from  what  has  been 
said  above  it  is  obvious  that  981  dynes  go  to 
one  gram,  or  981,000  dynes  (approximately 
one  million  dynes)  are  equivalent  to  the  kg. 
If  we  now  repeat  the  calculation,  using  the 
c.g.s.  system,  we  get  the  force  in  dynes  if  we 
express  in  the  general  formula 

„       .Mm 

a/-pr 

the  masses  in  grams  and  the  distance  in  cm. 
The  ethereal  coefficient  then  has  the  value 

/  =  6-6  X  10-8 


20  ELECTRICITY 

The  knowledge  of  this  coefficient  enables  us 
to  determine  for  any  two  bodies  the  attrac- 
tive force  if  their  masses,  configuration  and 
relative  position  are  given.  For  spheres  the 
calculation  is  quite  simple,  but  for  bodies  of 
more  complicated  shape  it  is  very  difficult, 
and  sometimes  only  possible  in  rough  approxi- 
mation. It  would,  for  instance,  hardly  be 
possible  to  accurately  calculate  the  mass  at- 
traction between  two  Dreadnoughts  lying  side 
by  side,  but  by  using  the  general  formula  and 
the  coefficient  /  as  here  determined  we  get  as  a 
rough  approximation  a  force  of  7  Ib. 

It  is,  of  course,  out  of  the  question  to  check 
such  a  calculation  by  direct  experiment,  since 
disturbing  causes,  such  as  the  slightest  breath 
of  wind  striking  the  side  of  the  ship,  will  pro- 
duce a  disturbing  force  many  times  greater 
than  the  force  to  be  measured.  If,  however, 
we  could  eliminate  all  disturbing  forces,  then 
a  direct  determination  of  /,  quite  independent 
of  astronomical  observation,  would  be  possible. 
Such  determinations  have  been  made  by 
Cavendish,  Maskelyne,  Airy  and  others,  the 
most  recent  being  Poynting's,  carried  out 
in  the  Birmingham  University.  Professor 
Poynting  has  measured,  by  means  of  an 
exceedingly  delicate  balance,  the  attractive 


ACTION  OF  FORCES  21 

force  between  two  lead  spheres  of  known  mass, 
and  has  thus  determined  /,  and  from  this  value 
he  found  the  mass  of  the  earth  to  be  6-6  x  1027 
grams.  In  popular  language,  he  has  weighed 
the  earth. 

The  reader  may  perhaps  ask  what  all  this 
has  to  do  with  electricity.  Nothing  directly. 
I  have  merely  introduced  the  subject  of  gravi- 
tation, which  is  familiar  to  all,  as  a  starting- 
point,  so  as  to  familiarise  the  reader  with  the 
conception  of  the  ethereal  coefficient;  and 
I  now  go  back  to  the  consideration  of  electric 
and  magnetic  forces  acting  across  space. 

I  assume  that  the  reader  is  familiar  with 
the  usual  textbook  explanation  of  how  bodies 
may  be  electrified,  or,  as  it  is  also  termed, 
charged  with  electricity.  Imagine  then  that 
we  have  given  electric  charges  to  two  spheres 
which  are  suspended  from  silk  threads.  Such 
suspension  is  necessary,  for  if  we  were  to 
handle  the  spheres  or  lay  them  on  to  the  table 
their  charges  would  leak  away;  if  we  wish  a 
body  to  preserve  its  charge  for  a  sensible  time 
we  must  support  it  by  an  insulator— such  as 
silk,  glass,  mica,  ebonite,  which  does  not  allow 
electricity  to  flow  along  or  through  it.  Metals 
offer  a  very  easy  path  for  the  flow  of  elec- 
tricity, and  are  therefore  called  conductors. 


22  ELECTRICITY 

There  is  no  sharp  line  of  demarcation  between 
insulators  and  conductors.  Dry  wood,  for 
instance,  is  not  a  perfect  insulator ;  and  when 
damp  it  is  not  a  perfect  conductor.  Dry  air 
at  atmospheric  pressure  is  almost  a  perfect 
insulator,  but  if  rarefied  or  at  high  temperature 
it  becomes  more  or  less  of  a  conductor.  All 
metals  are  conductors,  but  they  are  not  all 
equally  good  conductors.  Mercury  is  not  so 
good  a  conductor  as  iron,  iron  is  not  so  good 
as  copper,  and  silver  is  still  a  slightly  better 
conductor  than  copper.  The  difference  between 
the  two  last-named  metals  is,  however,  not 
great  enough  to  justify  commercially  the  use  of 
silver  instead  of  copper  wire  in  the  construc- 
tion of  electrical  machinery.  For  the  present 
we  need  not  inquire  further  into  any  fine 
gradations  between  conductors  and  insulators. 
We  assume  that  the  silk  threads  used 
for  the  suspension  of  the  charged  spheres 
and  the  air  surrounding  them  are  perfect 
insulators,  so  that  the  spheres  will  retain 
their  charges  as  long  as  they  do  not  come  into 
actual  contact  with  each  other  or  some  other 
conductor.  If  we  suspend  the  spheres  near 
each  other  we  find  that  they  do  not  hang 
plumb.  If  they  are  both  positively  or  both 
negatively  charged  the  distance  between 


ACTION   OF  FORCES  23 

their  centres  will  be  greater  than  the  distance 
between  the  points  of  suspension.  If  the 
charges  are  of  opposite  sign,  the  opposite  will 
be  the  case.  This  shows  respectively  that  a 
repulsive  force  and  an  attractive  force  is 
causing  the  deviation  from  the  vertical.  If 
we  know  the  weight  of  the  spheres,  measure 
their  distance  and  the  angle  of  deviation  of  the. 
suspending  threads  from  the  vertical,  the 
force  acting  between  the  two  charges  can  be 
calculated  from  well-known  mechanical  prin- 
ciples in  quite  a  simple  manner. 

It  is,  however,  necessary  to  avoid  disturbing 
influences.  The  spheres  must  hang  in  the, 
middle  of  a  very  large  room,  so  that  floor, 
ceiling  and  walls  are  far  removed,  and  we  must 
make  the  observations  by  telescope,  as  other- 
wise the  presence  of  the  body  of  the  observer 
near  the  spheres  would  disturb  the  electrical 
equilibrium.  I  need  hardly  say  that  such 
an  experiment  would  be  expensive  and 
difficult;  in  reality  it  need  not  be  made,  as 
there  are  other  far  more  practical  methods  of 
investigation  available,  but  it  is  convenient 
to  imagine  such  an  experiment,  because  it 
will  enable  me  to  explain  in  the  simplest 
possible  way  certain  first  principles.  Suppose 
then  that  we  are  not  deterred  by  questions  of 


24  ELECTRICITY 

cost  and  have  overcome  all  the  technical 
difficulties.  Let  us  first,  without  altering  the 
amount  of  charge  on  each  sphere,  merely 
shift  their  positions  so  as  to  get  different 
distances.  Measuring  the  force  in  each  case, 
we  will  find  that  this  force  varies  inversely 
as  the  square  of  the  distance.  We  have  thus 
verified  part  of  our  general  equation.  Now 
let  us  retain  one  particular  distance  and 
change  the  amount  of  charge,  first  on  one 
sphere  only  and  then  on  both.  We  find  that 
the  force  varies  directly  as  the  product  of 
the  two  charges.  This  experiment  confirms 
the  rest  of  the  equation. 

Writing  now  Q  and  q  for  the  quantity  of 
charge  on  each  sphere  the  general  equation 
takes  the  form  • 


In  the  case  of  both  spheres  containing 
equal  charges  this  may  also  be  written  as  an 
equation  between  the  product  of  F  and  D2  on 
the  one  hand,  and  /  and  Q2  on  the  other  — 

F  x  D2  =  /  x  Q2 

Suppose  we  have  succeeded  in  so  adjusting 
the  charges  that  F  x  D2  is  unity  ;  this  might 
be  the  case  for  D  =  10  cm.  and  F  =  y^  dyne, 


ACTION   OF   FORCES  25 

or  D  =  1  cm.  and  F  =  1  dyne.  The  product 
/  X  Q2  will  then  also  be  unity.  All  that  our 
experiment  tells  us  is  that  the  product  of 
two  things  is  unity,  but  it  does  not  tell  us 
the  separate  value  of  each  of  the  two  things, 
which  is  only  another  way  of  saying  that  we 
do  not  know  and  probably  shall  never  know 
what  electricity  really  is  any  more  than  we 
can  know  the  real  nature  and  value  of  the 
ethereal  coefficient.  We  can,  however,  choose 
one  of  the  factors,  and  then  the  other  is  also 
determined.  If  we  adopt  the  definition  of 
unit  mass  given  on  p.  13,  then  Q  is  1  and 
Q2  is  also  1.  From  this  it  follows  that  /  is  also 
1,  and  our  general  formula  simplifies  to 

F_Q? 

~D2 

In  adopting  this  formula  we  have  arbitrarily 
settled  the  magnitude  of  the  unit  of  electric 
quantity.  It  is  such  a  quantity  of  charge  as 
will  give  the  force  of  one  dyne,  if  acting  on  an 
equal  charge  at  a  distance  of  one  cm. 

It  will  be  noticed  that  the  train  of  reasoning 
followed  here  is  different  from  that  we  followed 
in  the  case  of  gravitation.  There  we  started 
by  adopting  a  particular  quantity  of  ponder- 
able matter  as  the  unit,  namely  the  gram. 
This  is  the  obvious  way,  because  we  know 


26  ELECTRICITY 

what  the  mass  of  a  gram  is  and  we  can  repro- 
duce it  at  any  time.  A  cubic  cm.  of  water  at 
four  degrees  C.  has  the  mass  of  one  gram. 
Having  thus  settled  the  magnitude  of  the 
mass  unit  we  determined  the  numerical  value 
of  the  ethereal  coefficient.  In  the  electrical 
case  we  settle  arbitrarily  the  value  of  the 
ethereal  coefficient  as  unity,  and  determine 
on  this  basis  the  magnitude  of  unit  electric 
quantity.  In  our  experiment  the  spheres  are 
at  rest,  there  is  no  flow  of  electricity,  and 
the  system  is  in  static  equilibrium. 

The  unit  of  charge  thus  denned  is  there- 
fore called  the  electrostatic  unit  of  electric 
quantity  in  the  c.g.s.  system.  In  our  experi- 
ment the  room  was  filled  with  air.  Let  us  now 
fill  the  room  with  oil.  Since  oil  is  an  excellent 
insulator  the  spheres  will  retain  their  charges, 
but  we  shall  observe  a  diminution  of  the  force. 
The  charge  on  each  sphere  has  not  altered, 
but  the  force  acting  between  them  has  become 
smaller.  We  have  settled  the  magnitude  of 
unit  quantity  in  such  way  that  the  coefficient 
/  in  air  shall  be  unity,  but  after  filling  the  room 
with  oil  we  find  that  this  coefficient  is  only 
say  J.  Whether  it  is  exactly  \  or  some 
other  fraction  depends  on  the  particular  kind 
of  oil  used.  To  treat  the  matter  quite 


ACTION  OF  FORCES  27 

generally  let  us  call  the  fraction  ™  The 
force  will  now  be  expressed  by  the  formula 

F-1Q? 
~K  D2 

K  being  a  number  depending  on  the  medium 
in  which  the  spheres  are  suspended.  This 
numeric  indicates  the  degree  of  attenuation  of 
the  force  brought  about  by  the  presence  of 
an  insulating  body  between  the  spheres. 
This  body,  which  separates  the  two  electrified 
bodies,  is  called  the  dielectric.  To  bring  back 
the  force  to  its  old  value  we  must  increase  the 
charges.  By  using  a  dielectric  we  have  en- 
abled the  spheres  to  hold  a  greater  charge 
without  exerting  on  each  other  a  greater  force. 
We  have  increased  their  capacity  for  storing 
a  charge,  and  for  this  reason  K  is  called  the 
specific  inductive  capacity  of  the  medium,  or 
also  the  dielectric  constant  of  the  medium. 
The  value  of  K  is  about  2  for  oil,  2  to  3  for 
paper,  6  for  mica,  and  may  go  up  to  as  much 
as  10  for  glass.  The  larger  K,  the  greater  is 
the  charge  with  a  given  force  pushing  the 
electricity  on  to  the  conductor.  This  force 
must,  however,  not  be  confounded  with  the 
mechanical  force  of  attraction  or  repulsion 


28  ELECTRICITY 

with  which  we  have  been  concerned  hitherto ; 
there  is  a  relation  between  the  two,  as  will  be 
explained  in  Chapter  III,  but  they  are  not 
identical. 

The  same  reasoning  as  above  applied  to 
electric  attraction  and  repulsion  may  also  be 
applied  to  forces  produced  by  magnetism, 
but  if  we  attempt  an  experimental  veri- 
fication of  the  general  law  of  forces  acting 
through  space  we  encounter  some  difficulty. 
When  dealing  with  electricity  it  is  quite  easy 
to  isolate  a  positive  from  a  negative  charge 
each  on  its  own  conductor,  or,  as  we  may  also 
term  it,  it  is  possible  to  accumulate  free  elec- 
tricity of  one  sign  on  a  conductor.  It  is  not 
possible  to  accumulate  only  north  magnetic 
matter,  or  only  south  magnetic  matter  on 
one  piece  of  steel.  We  always  get  magnetic 
matter  of  both  signs  simultaneously  on  the 
steel.  If  this  has  the  form  of  a  bar  we  can, 
by  stroking  it  with  a  loadstone,  make  one 
end  of  the  bar  a  north  pole  and  the  other  a 
south  pole,  but  if  we  break  the  bar  in  halves 
we  do  not  get  one  half  all  north  and  the  other 
all  south.  Each  half  again  shows  north  at 
one  end  and  south  at  the  other.  In  experi- 
menting on  magnetic  forces  we  are,  therefore, 
always  disturbed  by  the  presence  of  magnetic 


ACTION  OF  FORCES  29 

matter  of  the  opposite  polarity.  Another 
difficulty  lies  in  this,  that  the  magnetic  matter 
is  spread  over  the  whole  of  the  bar — more 
dense  at  the  ends,  but  still  of  sensible  density 
at  points  towards  the  middle.  Thus  it  becomes 
difficult  to  estimate  the  average  distance  of 
action.  These  difficulties  are  so  great  that 
the  same  methods  of  experimenting,  which 
we  supposed  to  be  used  when  investigating 
electric  forces,  become  quite  impracticable, 
and  other  methods  have  to  be  devised. 

These  methods  are  based  on  the  conception 
of  the  magnetic  moment,  that  is,  the  product 
of  the  distance  of  poles  into  their  strength. 
Any  physical  magnet  can  then  be  considered 
as  a  bundle  of  mathematical  magnets,  each 
carrying  magnetic  matter  only  at  the  extreme 
ends.  We  observe  experimentally  the  sum- 
marised effect  of  all  these  elementary  magnets, 
and  by  mathematical  reasoning  we  are  able 
to  deduce  the  law  under  which  magnetic 
forces  act  across  space.  Experiment  shows 
that  the  law  stated  in  the  beginning  of  this 
chapter  also  holds  good  for  magnetic  forces. 
Moreover,  the  magnitude  of  the  unit  of 
magnetism  may  be  determined  in  the  same 
way.  If  we  find  that  two  equally  strong 
poles  placed  one  cm.  apart  exert  on  each 


30  ELECTRICITY 

other  a  force  of  one  dyne,  then  each  contains 
unit  of  magnetic  matter.  This  definition 
again  means  that  we  have  arbitrarily  assumed 
the  ethereal  coefficient  of  air  to  be  unity. 

When  making  the  experiment  with  electric 
charges  we  found  that  by  filling  the  space 
between  the  active  charges  with  a  substance 
such  as  oil  or  glass,  the  force  was  diminished. 
No  such  effect  is  observable  with  magnets. 
We  may  put  them  under  oil  or  water,  or  we 
may  put  a  sheet  of  glass  between  them,  and 
we  shall  find  precisely  the  same  force.  If, 
however,  we  immerse  them  in  liquid  oxygen 
there  will  be  a  decrease  of  force,  and  if  such 
a  thing  as  an  iron  atmosphere  were  possible, 
the  decrease  in  such  an  atmosphere  would  be 
very  great.  We  may  therefore  say  that  the 
ethereal  coefficient  for  magnetic  forces  is 
unity  for  air,  oil,  wood  and  any  so-called 
non-magnetic  substance;  and  smaller  than 
unity  for  magnetic  substances  such  as  iron, 
nickel  and  cobalt.  If  we  try  the  experiment 
with  a  plate  of  bismuth  we  shall  find  a  slight 
increase  of  the  force,  showing  that  the  mag- 
netic ethereal  coefficient  for  bismuth  is  a 
shade  greater  than  unity,  the  value  assumed 
for  air.  For  iron  it  is  enormously  smaller. 
We  may  say  that  iron  is  more  permeable  to 


ACTION  OF  FORCES  31 

the  transmission  of  magnetic  forces  than  air 
or  brass  or  wood,  and  the  degree  to  which 
this  transmission  is  facilitated  is  called  the 
magnetic  permeability.  In  physical  and  en- 
gineering calculation  the  permeability  (which 
is  nothing  else  than  the  reciprocal  of  the 
ethereal  coefficient)  is  indicated  by  the  Greek 
symbol  //,  so  that  for  magnetic  forces  the 
general  equation  for  action  over  a  distance  D 
becomes 

,-,      1  Mm 

X!    =  —     T^O 
JLL     D2 

The  suitability  of  any  particular  kind  of 
iron  for  use  in  electrical  machinery  depends 
on  the  value  of  ^,  and  the  exact  determination 
of  this  ethereal  coefficient  thus  becomes  a 
matter  of  practical  importance.  In  making 
such  determinations  advantage  is  taken  of 
certain  relations  which  exist  between  elec- 
tricity in  the  flowing  state,  commonly  called 
electric  currents,  and  magnetic  effects.  Since 
any  flowing  current  represents  energy,  that 
is  to  say,  is  a  dynamic  phenomenon,  such 
experiments  have  an  electrodynamic  character, 
and  the  unit  of  magnetic  matter  as  defined 
above,  under  the  arbitrary  assumption  that 
the  magnetic  ethereal  coefficient  for  air  is 


32  ELECTRICITY 

unity,  is  called  the  c.g.s.  unit  of  magnetism  in 
the  electrodynamic  system. 

We  have  thus  two  different  systems  of 
measurement,  the  electrostatic  and  the  electro- 
dynamic.  They  have  been  adopted  as  a 
matter  of  convenience  in  order  to  be  able  to 
regard  in  both  the  ethereal  coefficient  of  air 
as  unity.  The  result  of  this  is  that  the 
absolute  magnitude  of  electric  quantity  in 
the  two  systems  is  very  different.  In  the 
electrostatic  system  unit  quantity  is  ex- 
ceedingly small  as  compared  to  the  amount  of 
electricity  which  goes  to  make  up  one  unit  of 
charge  in  the  electrodynamic  system.  It 
requires  30,000  millions  electrostatic  units 
to  make  up  one  electrodynamic  (or,  as  it  is 
also  called,  electromagnetic)  unit  of  electricity. 
The  speed  of  light  is  30,000  millions  cm.  per 
second.  It  is  highly  improbable  that  the 
agreement  between  the  speed  of  light  and  the 
numerical  ratio  between  the  units  should  be 
a  mere  coincidence ;  but  if  it  is  not,  then  the 
ratio  between  the  units  is  not  merely  a  numeric 
but  something  which  has  a  particular  char- 
acter, namely,  the  character  of  velocity,  that 
is,  a  length  divided  by  a  time.  Further,  if  we 
rule  out  the  idea  of  a  merely  accidental 
agreement  between  two  numbers,  we  are 


ACTION  OF  FORCES  33 

driven  to  the  conclusion  that  the  ether  is  the 
actual  carrier  of  force  and  energy ;  and  this  is 
the  conception  on  which  the  modern  science 
of  electricity  and  magnetism,  and  in  fact  the 
whole  structure  of  electrical  engineering,  is 
founded. 


CHAPTER  II 

ON  FRICTIONAL  AND   CONTACT   ELECTRICITY 

THE  distinction  generally  found  in  text- 
books on  physics  between  the  so-called 
"  f fictional  "  and  "  contact  "  electricity  does 
not  imply  that  there  are  two  different  kinds 
of  electricity,  but  it  refers  to  two  different 
methods  of  producing  electrification  of  bodies. 
Besides  these  two  there  are  other  methods, 
and  some  of  them  are  of  much  greater 
practical  importance.  Those  will  be  dis- 
cussed in  subsequent  chapters ;  for  the  present 
we  restrict  the  discussion  to  the  two  methods 
mentioned  above. 

The  term  "  frictional  electricity  "  indicates 
the  process  by  which  the  electrification  of 
a  body  is  produced.  If  a  stick  of  sealing-wax 
is  rubbed  with  a  flannel,  both  these  bodies 
show  electrification,  but  of  opposite  sign. 
We  agree  to  call  the  electricity  residing  on 
the  sealing-wax  negative,  and  that  on  the 
flannel  positive.  Electricity  may  also  be 
34 


FRICTIONAL  AND   CONTACT     35 

produced  by  rubbing  a  glass  rod  with  a  pad 
of  leather,  which  has  been  covered  with  a 
mercury  amalgam  of  zinc.  In  this  case  the 
glass  rod  shows  positive  electrification,  and 
the  pad  negative.  The  old  physics  text- 
books, therefore,  also  speak  of  a  "  vitreous  " 
and  a  "  resinous  "  electricity,  meaning  thereby 
respectively  electric  charges  of  positive  and 
negative  sign.  The  electrification  is  the 
result  of  friction  between  two  different  sub- 
stances, one  becoming  positively  and  the 
other  negatively  charged.  Probably  any  pair 
of  bodies  can  thus  be  electrified,  provided 
the  necessary  care  is  taken  to  prevent  the 
accumulated  charge  leaking  off.  The  process 
is  not  even  restricted  to  solids;  the  friction 
between  a  solid  and  a  gas  also  produces 
electrification.  This  fact  is  utilised  in  the 
Armstrong  electric  machine,  where  jets  of 
steam  are  caused  to  flow  past  the  spikes  of 
a  metal  comb.  By  the  friction  of  the  steam 
against  the  surface  of  the  metal  the  latter 
becomes  electrified.  It  is  also  well  known 
that  the  friction  of  the  gas  escaping  through 
the  valve  of  a  balloon  produces  electrification 
of  the  envelope,  and  under  certain  circum- 
stances so  strong  an  electrification  that  a 
spark  discharge  may  occur.  This  danger^  is 


36  ELECTRICITY 

avoided  by  the  use  of  the  ripping  line  on 
landing.  The  escape  of  gas  then  takes  place 
through  so  large  an  opening  that  the  velocity 
with  which  the  gas  passes  the  edges  of  the 
orifice  is  small,  and  the  friction  not  sufficient 
to  produce  a  sparking  charge. 

The  friction  between  a  pulley  and  its  belt 
may  in  a  dry  atmosphere  produce  so  strong 
a  charge  in  the  belt  that  sparks  may  be 
drawn  from  it.  Such  sparks  are  quite  harm- 
less to  any  person  struck  by  them,  but  they 
may  become  a  source  of  danger  if  inflammable 
substances  are  near.  Thus  in  paper-making 
machinery,  where  the  band  of  paper  passes 
at  high  speed  over  hot  metal  rolls,  it  may 
become  electrified  to  the  extent  of  sparking 
and  igniting  itself.  To  avoid  this  danger  it 
is  necessary  to  fix  spiked  combs,  which  draw 
off  the  charge  as  soon  as  generated.  In 
all  these  cases  the  electricity  produced  by 
friction  is  only  an  inconvenient  by-product 
of  some  other  operation;  but  if  we  wish  to 
produce  electricity  for  experimental  work 
we  may  use  special  appliances  based  on  the 
principle  of  electrification  by  friction.  These 
are  called  "  frictional  machines."  In  sub- 
stance they  are  nothing  more  than  elabora- 
tions of  the  primitive  glass  rod  and  leather 


FRICTIONAL  AND  CONTACT       37 

pad,  so  that  the  friction  may  take  place 
under  a  suitable  pressure  and  with  sufficient 
speed.  The  machine  is  also  fitted  with  spiked 
combs  for  taking  off  the  negative  charge  from 
the  pad  and  the  positive  from  the  glass,  and 
generally  there  is  some  contrivance  added  for 
storing  the  charges,  or  one  of  them.  Machines 
of  this  kind  are  very  inefficient,  and  as  they 
have  within  our  generation  been  superseded  by 
much  more  efficient  machines  working  on  a 
different  principle,  which  are  treated  in  the 
fourth  chapter,  we  need  not  discuss  them  in 
detail. 

The  frictional  machine  was,  however,  up  to 
the  year  1789  the  only  practical  means  of 
producing  such  electrification  as  the  physic- 
ist of  those  days  required  for  his  experiments. 
In  that  year  there  came  a  change.  L.  Galvani, 
Professor  at  the  Bologna  University,  found 
that  electric  effects  could  be  produced  in 
animal  tissue,  if  this  were  put  into  contact 
with  two  different  metals,  in  his  case  copper 
and  iron.  His  experiment  with  the  frogs' 
legs  is  so  well  known  that  it  would  be  wasting 
space  to  describe  it  here.  Galvani  looked 
for  the  cause  of  the  phenomena  observed  in 
the  tissue  and  not  in  the  metals.  In  this  he 
was  mistaken.  He  assumed  the  existence  of 


38  ELECTRICITY 

some  mysterious  "  electric  life  force,"  and 
the  name  of  "  Galvanism  "  was  given  by  the 
scientists  of  the  time  to  this  supposed  force. 
This  term  has  survived  even  to  this  day, 
though,  except  in  some  medical  writings, 
rather  in  a  metaphorical  than  a  scientific 
sense. 

Galvani's  conception  of  an  electric  life 
force  held  the  field  for  only  a  short  time; 
it  was  proved  to  be  a  misconception  by 
Alexander  Volta,  Professor  at  the  Pavia 
University,  who  showed  by  a  conclusive  experi- 
ment that  the  cause  of  electrification  does 
not  reside  in  the  animal  tissue  at  all,  but  in 
the  contact  between  the  two  different  metals. 
He  took  discs  of  different  metals,  such  as 
copper  and  iron  or  copper  and  zinc,  and  laid 
one  on  the  other.  The  discs  must  be  perfectly 
flat  so  as  to  present  to  each  other  even  contact 
surfaces.  Volta  in  his  classic  experiment 
found  that  such  discs,  if  separated  after 
having  been  in  contact  for  ever  so  short  a 
time,  show  signs  of  electrification;  one  being 
positively,  the  other  negatively  charged.  In 
this  experiment  there  is  no  question  of  any 
life  force  residing  in  animal  tissue,  for  no 
such  tissue  is  being  used.  The  discs  are 
simply  laid  one  on  the  other,  touched  on 


FRICTIONAL  AND   CONTACT       39 

the  back,  and  then  separated.  Volta  recog- 
nised that  the  cause  of  electrification  was 
the  contact  pure  and  simple  between  the 
two  dissimilar  metals,  and  for  this  reason 
we  may  speak  of  "  contact  electricity  "  or 
"  voltaic  electricity  "  when  we  mean  the  kind 
of  electrification  first  discovered  by  Volta. 

Various  theories  have  been  set  up  to  ex- 
plain what  may  be  termed  the  mechanism  of 
this  electrification.  According  to  Helmholz, 
the  molecules  of  a  metal  are  endowed  with 
the  ability  to  attract  and  hold  both  electri- 
cities, but  not  with  equal  force.  These  mole- 
cular forces  are  different  in  different  metals, 
and  in  consequence  of  these  differences  there 
takes  place  an  actual  separation  between  the 
two  electricities  at  the  boundary  surface 
between  the  two  metals.  Other  scientists 
(notably  De  la  Rive)  doubt  the  existence  of 
such  a  molecular  force  in  the  metal  itself,  and 
look  for  the  cause  of  electrification  in  the 
influence  of  an  intervening  link  between  the 
two  metals,  namely,  the  moisture  of  the 
atmosphere.  They  point  out  that  even  with 
the  most  accurate  ground  surfaces  it  is 
obviously  impossible  to  make  molecular  con- 
tact between  the  two  metals ;  that  there  must 
always  be  interposed  a  film  of  gases  and 


40  ELECTRICITY 

vapours,  and  that  it  is  by  the  intervention 
of  this  gaseous  connecting  link  that  the 
phenomenon  called  contact  electricity  takes 
place. 

Whether  the  one  set  of  theorists  or  the 
other  have  come  near  a  true  explanation, 
or  whether  both  are  mistaken,  is  not  a  matter 
which  need  concern  us;  the  important  fact 
is  that  electrification  is  produced  by  the  con- 
tact between  two  metals,  and  that  the  in- 
tensity of  their  electrification,  or  the  force 
by  which  the  two  electricities  are  separated 
across  the  boundary  line  of  the  two  surfaces, 
does  not  depend  on  the  extent  of  the  surface 
of  contact,  but  only  on  the  quality  of  metals 
used  in  the  combination.  The  force  is  greater 
with  some  combinations  and  smaller  with 
others.  By  testing  various  combinations,  it 
is  thus  possible  to  range  all  metals  in  a  series, 
in  which  that  metal  which,  combined  with 
any  other  always  shows  a  positive  charge, 
stands  at  one  end.  This  had  already  been 
done  by  Volta  himself,  who  gave  the  series  : 
ZINC — LEAD — TIN — IRON —  COPPER  —  SILVER 
— GOLD.  Zinc  stands  at  the  positive,  and 
gold  at  the  negative  end  of  the  series.  This 
sequence  has  been  verified  by  all  later  ob- 
servers, who  have  also  confirmed  another 


FRICTIONAL  AND   CONTACT       41 

observation  originally  made  and  published 
by  Volta,  namely,  that  the  electric  force 
between  any  two  metals  in  the  series  is  equal 
to  the  sum  of  the  electric  forces  between  all 
intermediate  pairs.  Thus,  if  in  any  arbitrary 
scale  the  electric  force  between  zinc  and  lead 
is  2,  and  that  between  lead  and  copper  5, 
then  the  electric  force  between  zinc  and 
copper  is  2  -f  5  =  7. 

The  series  given  above  ends  with  the  most 
negative  metal — gold ;  but  Volta  found  that 
another  substance,  not  a  metal,  but  graphite, 
which  is  a  special  form  of  carbon,  is  still 
more  negative  than  gold,  and  since  Volta's 
time  the  series  has  been  enlarged  and  extended 
by  the  addition  of  other  metals  and  also 
sulphates  and  oxides,  so  that  we  must  con- 
sider the  phenomenon  of  electrification  by 
contact  to  extend  over  a  great  variety  of 
substances,  and  not  to  be  restricted  to  a 
combination  of  metals. 

Whether  electrification  is  produced  by 
friction  or  by  contact,  the  process  is  in  either 
case  the  separation  of  charges  of  electricity  of 
opposite  sign.  We  know  that  such  charges 
attract  each  other,  and  that  if  accumulated 
on  conductors  sufficiently  near,  the  conductors 
themselves  will  experience  an  attracting  force. 


42  ELECTRICITY 

The  tendency  will  be  to  bring  the  conductors 
together,  and  if  they  are  held  firmly  in  place, 
the  tendency  will  be  for  the  charges  them- 
selves to  leave  the  conductors  and  unite. 
Whether  they  will  actually  do  this  depends 
on  the  distance  between  the  nearest  points 
of  the  conductors  and  the  strength  of  the 
charges  accumulated  on  them.  Under  certain 
conditions  the  force  of  attraction  may  be 
sufficiently  great  and  the  distance  sufficiently 
small  to  cause  electricity  to  leap  across 
the  intervening  space,  and  then  we  have 
the  familiar  phenomenon  of  an  electric 
spark. 

The  same  phenomenon  is  observed  in 
lightning,  in  which  case  the  conductors  may 
be  two  clouds  charged  with  electricity,  or  a 
cloud  and  the  earth.  The  force  which  in  an 
electric  machine  causes  the  separation  be- 
tween positive  and  negative  electricity  is 
called  the  "  electromotive  force,"  and  the 
practical  unit  in  which  the  magnitude  of 
electromotive  force  is  expressed  is  called  the 
"volt."  To  give  the  reader  an  idea  of  the 
size  of  this  unit  it  may  be  mentioned  that 
the  electromotive  force  (or  e.m.f.)  with  which 
electricity  is  caused  to  flow  through  an 
incandescent  lamp  is  of  the  order  of  100  to 


FRICTIONAL  AND  CONTACT       43 

250  volts,  according  to  the  type  of  lamp 
used.  The  most  prevalent  voltage  employed 
for  domestic  lighting  is  220  v.  In  com- 
parison with  this  the  e.m.f.  of  contact  is 
very  small,  and  that  produced  in  a  frictional 
machine  is  prodigiously  large.  The  latter 
may  easily  reach  tens  of  thousands  or  even 
hundreds  of  thousands  of  volts,  whilst  the 
e.m.f.,  under  which  lightning  flashes  occur, 
may  be  many  millions  of  volts.  Between 
the  process  of  producing  electrification  by 
friction  and  producing  it  by  contact,  there  is 
thus  an  enormous  difference  in  degree,  but 
no  difference  in  kind,  both  processes  being 
simply  directed  to  the  separation  and  isolation 
of  charges  of  different  sign. 

If  the  positive  and  negative  conductors  of 
a  frictional  machine  are  connected  by  a 
wire,  the  charges  rush  along  this  wire  to  equal- 
ise each  other,  leaving  both  conductors  with- 
out charge.  We  may  imagine  a  simultaneous 
movement  of  positive  and  negative  electricity 
along  this  wire  in  opposite  directions,  or  we 
may  imagine  only  the  positive  charge  flowing 
along  the  wire  in  the  direction  of  the  negative 
conductor  and  spreading  itself  over  its  surface, 
and  thereby  neutralising  the  negative  charge 
previously  accumulated  on  it.  What  pre- 


44  ELECTRICITY 

cisely  takes  place  we  do  not  know,  but  as  a 
matter  of  convenience  we  assume  that  there 
is  only  one  current,  namely,  that  which  flows 
from  the  positive  to  the  negative  conductor, 
much  in  the  same  way  as  water  will  always 
flow  from  the  higher  to  the  lower  level. 

Electricity,  being  an  imponderable  entity 
(in  reality  merely  a  form  of  energy),  cannot  be 
connected  mentally  with  any  conception  of 
level,  such  as  is  legitimate  in  the  study  of  the 
movement  of  heavy  bodies.  Nevertheless  it 
is  convenient  to  introduce  a  somewhat  ana- 
logous conception  to  "  high  "  and  "  low  " 
when  dealing  with  electrical  problems,  and 
this  conception  is  that  of  "  electric  potential." 
Just  as  water  tends  to  flow  from  the  higher 
level  to  the  lower  level,  so  positive  electricity 
has  the  tendency  to  flow  from  the  conductor 
of  higher  to  that  of  lower  potential.  The 
mechanical  meaning  of  the  term  potential 
will  be  discussed  in  the  following  chapter; 
for  the  present  it  must  suffice  to  note  that 
as  long  as  the  two  conductors  are  kept  at  a 
difference  of  potential  by  the  working  of  the 
frictional  machine,  a  current  of  electricity 
will  flow  from  the  positive  to  the  negative 
conductor  through  the  wire  joining  them. 

The  current  obtainable  from  such  a  machine 


FRICTIONAL  AND   CONTACT       45 

is  exceedingly  small,  and  any  attempt  to 
produce  the  electric  currents  required  for 
lighting  or  other  technical  purposes  by  the 
use  of  a  frictional  machine  is  foredoomed  to 
failure.  Where  currents  of  any  magnitude 
are  required,  we  must  use  other  methods  of 
producing  electricity.  These  will  be  dis- 
cussed subsequently,  but  for  the  present  it 
is  important  to  note  that,  apart  from  a 
question  of  degree,  the  frictional  machine  is 
an  apparatus  whereby  electric  currents  may 
be  generated. 

How  does  the  matter  stand  with  regard 
to  electrification  by  contact  between  solid 
bodies  ?  Can  we  thereby  also  produce  an 
electric  current  ?  We  have  seen  that  two 
metals  in  contact  electrify  each  other.  Using 
copper  and  zinc,  the  former  becomes  nega- 
tively and  the  latter  positively  electrified; 
that  is  to  say,  the  zinc  becomes  the  body  of 
higher  and  the  copper  that  of  lower  potential, 
and  at  first  sight  it  might  appear  that  by 
joining  the  back  of  the  zinc  disc  to  the  back 
of  the  copper  disc  by  a  wire,  we  should  get 
a  current  flowing  along  this  wire  from  zinc 
to  copper.  This  is,  however,  not  the  case. 

Whatever  the  material  of  the  joining  wire 
may  be,  it  must  fall  somewhere  into  the 


46  ELECTRICITY 

series  of  contact  e.m.f.,  and  be  subjected 
to  the  law  that  the  sum  of  its  potential 
differences  to  zinc  on  the  one  side  and  to 
copper  on  the  other  side  is  equal  to  the 
potential  difference  between  zinc  and  copper. 
We  thus  have  a  perfect  balance  of  e.m.f.'s 
set  up  by  the  direct  contact  between  the 
two  discs  and  the  indirect  contact  via  the 
joining  wire.  Since  the  e.m.f.'s  are  in  equi- 
librium, no  current  can  flow.  If  it  were 
possible  to  upset  this  equilibrium  on  one  side 
or  the  other,  then  we  could  produce  a  current, 
and  that  is  actually  done  by  an  arrangement 
of  substances,  some  of  which  fall  outside  the 
series  of  contact  e.m.f.'s.  Such  arrangements 
are  called  "  voltaic  cells."  A  familiar  example 
is  the  so-called  Leclanch6  cell  (named  after 
its  inventor),  which  is  found  in  almost 
every  household  for  the  working  of  electric 
bells. 

Before  entering  on  a  study  of  voltaic  cells 
it  will  be  convenient  to  amplify  the  series 
on  p.  40  by  the  definite  statement  of  the 
e.m.f.  to  be  obtained  with  any  combination 
of  the  metals.  The  figures  in  the  following 
table  represent  experimental  results  obtained 
by  Ayrton  and  Perry,  and  recorded  in 
Whetham's  Practical  Electricity — 


FRICTIONAL  AND  CONTACT       47 


TABLE  OF  CONTACT  E.M.F.  IN  VOLTS 

(Zinc  is  positive  in  relation  to  all  the  other  substances 
given  in  this  table.) 


Substance. 

Zinc. 

Lead. 

Tin. 

Iron. 

Copper. 

Plati- 
num. 

Carbon. 

Zinc     . 

0 

0-210 

0-279 

0-592 

0-738 

0'976 

1-089 

Lead    . 

-  0-210 

0 

0-069 

0-382 

0-528 

0-766 

0-879 

Tin  .    . 

-  0-279 

-  0-069 

0 

0-313 

0-459 

0-697 

0-810 

Iron     . 

-  0-592 

-  0-382 

-  0-313 

0 

0-146 

0-384 

0-497 

Copper 
Platinum 

-  0-738 
-  0-976 

-  0-528 
-0-766 

-  0-495 
-  0-697 

-  0-146 
-  0-384 

0 

-  0-238 

0-238 
0 

0-351 
0-113 

Carbon 

-1-089 

-0-379 

-  0-810 

-  0-497 

-  0-351 

-  0-113 

0 

We  have  seen  that  no  current  due  to  contact 
e.m.f.  can  be  produced  in  a  circuit  the 
members  of  which  all  belong  to  a  series  of 
contact  e.m.f.,  and  which  therefore  fall  under 
the  law  that  the  potential  difference  between 
any  two  is  equal  to  the  sum  of  the  potential 
differences  of  the  intervening  pairs.  Which- 
ever way  we  go  round  such  a  circuit  the  total 
e.m.f.  is  always  zero.  To  get  an  e.m.f.,  and 
therefore  a  current  in  the  circuit,  we  must 
find  some  conducting  material  which  falls 
outside  the  series  in  the  sense  that  it  does  not 
obey  the  law  just  stated.  If  the  continuity 
of  metallic  contacts  is  interrupted  by  the 
interposition  of  such  a  material,  then  there 
will  be  no  complete  equilibrium,  but  a  balance 
of  e.m.f.  in  a  definite  direction  and  a  current 
will  result.  Water  is  such  a  material;  it 


48 


ELECTRICITY 


becomes  strongly  positive  when  in  contact 
with  any  of  the  substances  given  in  the  table, 
but  the  difference  of  e.m.f.  of  the  two  com- 
binations, water-zinc  and  water-copper,  is  not 
equal  to  that  of  the  combination  copper-zinc. 
Assume  for  the  moment  that  the  differ- 
ence is  zero,  or,  in  other  words,  that  water 


In 


FIG.  1. 

is  quite  inert  as  regards  contact  e.m.f.  and 
simply  acts  as  a  conductor.  This  is  not 
actually  the  case,  but  a  convenient  assump- 
tion for  the  purpose  of  explaining  the  way 
a  cell  may  give  an  e.m.f.  in  an  external  circuit. 
Let,  in  Fig.  1,  Zn  and  Cu  be  a  zinc  and  copper 
plate  respectively,  and  let  to  these  plates  be 
fastened  strips  of  copper  for  the  attachment 
of  the  terminals  A  and  B.  The  plates  are 


FRICTIONAL  AND   CONTACT       49 

not  directly  in  contact,  but  are  placed  in  a 
vessel  filled  with  water.  As  we  are  only 
dealing  with  potential  differences,  we  may 
arbitrarily  fix  the  potential  of  one  terminal 
at  zero.  Let  this  be  the  end  of  the  copper 
strip  soldered  at  a  to  the  zinc  plate.  Then 
the  potential  of  the  zinc  plate,  which  is  due 
to  the  contact  e.m.f.  of  the  junction  a  where 
the  copper  strip  is  soldered  to  it,  will  by  the 
table  on  p.  47  be  0-738  volts.  Since  by 
hypothesis  the  water  is  inert  both  as  regards 
the  zinc  and  the  copper,  this  will  also  be 
the  potential  of  the  copper.  The  junction 
at  b  cannot  alter  this  value,  since  at  that  place 
two  equal  metals  are  in  contact.  The  potential 
at  B  is  therefore  also  0-738  volts,  and  on 
joining  A  with  B  by  a  wire  a  current  will 
flow.  Now  let  us  replace  the  water  by  a 
dilute  solution  of  sulphuric  acid.  The  differ- 
ence of  contact  e.m.f.  of  this  liquid  in  relation 
to  zinc  on  the  one  hand  and  copper  on  the 
other  is  about  one-third  of  a  volt,  and  this 
difference  acts  in  the  same  sense  as  the 
contact  e.m.f.  at  a.  The  result  is  that  the 
potential  of  the  copper  plate,  and  therefore 
also  of  its  terminal  B,  has  now  been  increased 
to  a  little  over  one  volt.  Here  we  have  a 
combination  of  substances,  which,  by  virtue 
D 


50  ELECTRICITY 

of  contact  e.m.f .,  are  causing  a  current  to  flow. 
In  this  primitive  form  the  arrangement  is, 
however,  very  imperfect. 

As  soon  as  the  current  flows,  there  come 
into  play  some  secondary  actions,  which  cause 
the  contact  e.m.f.  between  zinc  and  liquid, 
which  is  in  a  forward  direction,  to  decrease, 
and  that  between  liquid  and  copper,  which  is 
in  a  backward  direction,  to  increase.  The  con- 
tact e.m.f.  causes  the  current  to  flow,  but  as 
soon  as  the  current  flows,  this  current  itself 
reduces  the  contact  e.m.f.  This  reaction 
may  be  illustrated  in  a  homely  way  by 
saying  appetite  causes  a  man  to  eat,  but 
when  eating  he  loses  his  appetite. 

This  interdependence  between  cause  and 
effect  is  observable  in  all  physical  processes, 
and  in  its  bearing  upon  the  relation  between 
electric  currents  and  mechanical  forces  it  has 
been  formulated  by-  Lenz,  and  is  known  as 
Lenz's  law.  Here  we  have  to  do  not  with 
mechanical,  but  with  chemical  forces.  The 
current,  in  passing  through  the  liquid,  de- 
composes it,  sending  oxygen  to  the  zinc,  which 
is  dissolved,  and  hydrogen  to  the  copper, 
where  it  forms  a  coating  and  introduces  an 
additional  counter  e.m.f.  of  contact.  This 
process  is  technically  termed  "  polarisation  " 


FRICTIONAL  AND  CONTACT       51 

of  a  cell,  and  the  ingenuity  of  inventors  has 
been  and  is  even  at  the  present  day  exercised 
in  finding  means  to  avoid  or  at  least  reduce 
the  effect  of  polarisation. 

The  first  and  completely  successful  attempt 
in  this  direction  has  been  made  by  Daniell,  in 
1836.  He  recognised  that  the  cure  for  polar- 
isation lay  in  preventing  any  hydrogen  being 
liberated  and  carried  to  the  copper  plate.  If 
the  liquid  in  the  immediate  vicinity  of  the  cop- 
per plate  contained  a  copper  salt,  it  would  not 
be  hydrogen  molecules,  but  copper  molecules 
that  are  precipitated  on  the  copper  plate,  and 
this  could,  of  course,  not  alter  the  original 
condition  of  the  cell.  He  used,  therefore, 
a  solution  of  sulphate  of  copper  as  the  liquid 
into  which  the  copper  plate  is  immersed. 
But  now  arises  another  difficulty.  We  must 
not  let  the  copper  sulphate  come  into  contact 
with  the  zinc,  for  this  would  not  give  the 
desired  e.m.f.,  and  it  would  also,  by  reason 
of  the  dissolution  of  the  zinc,  very  quickly 
spoil  the  solution.  It  is  thus  necessary  to 
still  use  dilute  sulphuric  acid  as  the  liquid 
into  which  the  zinc  is  immersed,  and  at  the 
same  time  anything  like  a  mixing  of  the  two 
liquids  must  be  avoided.  This  object  is 
attained  by  the  employment  of  a  porous  pot 


52  ELECTRICITY 

for  the  separation  of  the  two  liquids.  The 
porous  pot  forms  the  inner  vessel  into  which 
the  acid  and  zinc  are  placed,  whilst  an  outer 
vessel  is  provided  for  the  reception  of  the 
copper  plate,  and  the  solution  of  copper 
sulphate.  It  is  advisable  to  amalgamate  the 
zinc  with  mercury  so  as  to  protect  it  against 
attack  by  the  acid  when  the  cell  is  not  work- 
ing. When  it  is  working  no  protection  is 
possible,  for  the  electrochemical  action  must 
be  going  on  as  long  as  the  current  flows. 
By  this  action  oxygen  is  carried  to  the  zinc, 
and  this  is  thereby  dissolved,  forming  with 
the  sulphuric  acid  zinc  sulphate.  Thus  the 
electrical  energy  given  by  the  cell  to  the  ex- 
ternal circuit  is  obtained  at  the  cost  of  the 
chemical  energy  liberated  in  the  oxydation 
of  the  zinc  and  its  conversion  into  sulphate. 
The  e.m.f .  of  the  Daniell  cell  is  quite  constant ; 
it  is  a  little  over  one  volt. 

Since  DanielPs  time  many  types  of  de- 
polarising cells  have  been  invented,  zinc  being 
generally  one  of  the  metals  employed.  The 
current  passes  from  the  zinc  through  the 
liquid  to  the  other  plate,  which  may  be  of 
copper,  as  in  the  Daniell  and  Meidinger  cell, 
or  of  platinum  as  in  Grove's,  or  of  carbon  as 
in  Bunsen's  and  others.  Since  the  current 


FRICTIONAL  AND   CONTACT       53 

issues  from  the  cell  at  the  platinum  or  carbon 
plate,  the  terminal  in  connection  with  this 
plate  is  called  the  positive  pole  of  the  cell, 
the  zinc  terminal  being  the  negative  pole. 

One  of  the  most  largely  used  types  of  cell 
with  zinc-carbon  electrodes  is  that  designed 
by  Leclanche.  The  liquid  used  in  this  cell 
is  a  dilute  solution  of  salammonia,  and  the 
polarisation  of  the  carbon  is  counteracted  by 
the  employment  of  a  metallic  oxide  in  contact 
with  it.  The  carbon  plate  is  placed  into  a 
porous  pot  and  packed  round  tightly  with 
a  mixture  of  granular  gas  coke  and  manganese 
peroxide.  This  substance  is  a  powerful  oxy- 
dising  agent;  it  gets  hold  of  the  molecules 
of  hydrogen  on  their  way  to  the  carbon 
electrode,  and  thus  prevents  them  settling 
there  and  causing  a  back  e.m.f.  of  polarisa- 
tion. This  chemical  action  can,  however,  only 
go  on  at  a  moderate  rate,  so  that  the  Leclanche* 
cell  is  mostly  used  where  weak  and  inter- 
mittent currents  are  required,  as  for  instance, 
in  the  working  of  electric  bells.  If  the  cell 
is  worked  too  hard,  the  chemical  action, 
whereby  polarisation  is  rendered  innocuous, 
cannot  keep  pace  with  the  rate  at  which 
hydrogen  is  carried  to  the  carbon  plate,  and 
the  e.m.f.  of  the  cell,  which  under  normal 


54  ELECTRICITY 

conditions  is  about  1-4  volts,  drops  to  a  much 
smaller  figure.  If  left  standing  idle  a  little 
while,  the  cell  recovers  and  its  e.m.f.  rises 
again  to  1/4  volts.  It  will  be  obvious  that 
by  joining  up  in  the  same  sense  a  sufficient 
number  of  Daniell  cells,  or  cells  of  any  other 
type,  any  desired  voltage  may  be  obtained 
between  the  ends  of  the  series  of  cells. 

A  special  type  of  cell  is  the  so  called  accumu- 
lator or  storage  cell,  in  which  both  electrodes 
are  lead  and  some  oxide  of  lead.  This  is  a 
so-called  reversible  cell.  On  forcing  a  current 
through  in  one  direction,  the  oxide  on  the 
plate  where  the  current  enters  the  electrolyte 
(dilute  sulphuric  acid)  is  reduced,  and  the 
other  electrode  becomes  more  highly  oxidised. 
Thus  the  cell  is  charged.  If  then  the  cell  is 
connected  to  any  working  circuit,  it  gives  a 
current  in  the  reverse  direction  ;  the  previously 
strongly  oxidised  electrode  being  reduced  and 
the  other  becoming  more  oxidised,  the  cell 
discharges.  These  lead  accumulator  cells  are 
made  up  into  storage  batteries,  which  are  ex- 
tensively used  in  electricity  works. 


CHAPTER  III 

ON   POTENTIAL 

IN  the  first  chapter  we  investigated  in  a 
general  way  the  force  acting  between  two 
bodies,  and  we  found  that  this  force  may  be 
expressed  by  a  mathematical  formula  which 
is  the  same  for  real  masses,  electricity  and 
magnetism.  The  units  as  regards  length, 
time  and  force  may  be  the  same  in  all  cases, 
but  the  units  in  which  we  express  the  amount 
of  active  matter  producing  the  force  must 
naturally  be  different  in  each  case.  We  have 
also  seen  that  the  nature  of  the  medium  across 
which  the  force  acts  is  immaterial  in  the  case 
of  gravitation,  but  may  modify  the  force  in 
the  case  of  electricity  and  magnetism.  Let 
us  now,  without  for  the  moment  specifying 
any  particular  kind  of  active  matter,  assume 
that  one  of  the  bodies  contains  a  large  amount 
of  active  matter,  say  M  units,  and  that  the 
other  contains  one  unit  only.  For  brevity 
I  shall  call  them  the  large  and  the  small 
body.  We  can  then  use  the  small  body  to  in- 

$5 


56  ELECTRICITY 

vestigate  the  properties  of  the  space  surround- 
ing the  large  body.  In  this  investigation  the 
only  variables  are  the  force  and  the  distance 
from  the  active  centre  of  M,  the  force  being 
always  directed  either  towards  or  from  that 
point. 

The  force  may  thus  be  considered  as  an 
attribute  of  space,  and  it  becomes  possible, 
even  if  M  itself  is  inaccessible,  to  determine  its 
magnitude  and  location  by  measuring  the  direc- 
tion and  magnitude  of  the  force  experienced  by 
unit  matter  in  different  parts  of  space.  It  is 
not  even  necessary  that  the  measurements 
should  be  made  on  unity  of  active  matter ;  any 
convenient  quantity  of  active  matter  in  the 
small  body  will  serve.  All  we  need  do  is  to 
reduce  the  measured  force  in  the  ratio  of 
the  actual  amount  of  active  matter  used  to 
its  unit  value.  It  is  in  this  manner  that 
astronomers,  by  observing  disturbances  in  the 
orbit  of  a  known  star,  can  predict  the  exist- 
ence of  some  heavenly  body  not  yet  dis- 
covered by  the  telescope.  The  astronomical 
problem  is  exceedingly  complicated  because 
of  disturbances  from  other  active  masses  for 
which  allowance  has  to  be  made,  but  in 
studying  the  same  problem  as  applied  to 
electric  charges  no  such  complication  need 


ON  POTENTIAL  57 

arise.  We  can  so  devise  the  conditions  of 
the  experiment  that  no  other  force  than 
that  acting  between  the  large  and  the  small 
body  is  present.  The  condition  that  one 
body  should  contain  a  charge  large  in  com- 
parison with  the  other  is  not  essential,  only 
convenient,  as  it  obviates  the  necessity  of 
making  mathematical  corrections  which  would 
be  necessary  if  the  small  body  contained  a 
charge  of  the  same  order  of  magnitude.  In 
this  case  the  assumption  that  the  charge 
distributed  over  the  surface  of  a  sphere  acts 
in  the  same  way  as  if  it  were  concentrated 
in  the  centre  is  no  longer  strictly  true  for 
small  distances,  so  that  certain  corrections 
become  necessary. 

The  first  physicist  who  investigated  quanti- 
tatively the  action  of  electric  and  magnetic 
forces  across  space  was  Coulomb,  who  to- 
wards the  end  of  the  eighteenth  century 
invented  for  this  purpose  an  instrument  known 
as  the  torsion  balance.  As  applied  to  electric 
measurements,  it  consists  essentially  of  a  very 
light  scale  beam  made  of  sealing-wax  and  glass 
fibres,  and  suspended  horizontally  from  a 
thin  wire  attached  to  its  middle.  One  end 
of  the  beam  carries  a  gilded  pith  ball,  and  the 
other  a  mica  disc  as  a  counterweight.  The 


58  ELECTRICITY 

beam  cannot  dip  either  way,  but  it  can  be 
set  into  different  angular  positions  by  giving 
a  twist  to  the  upper  end  of  the  suspending 
wire,  or  if  the  upper  end  of  the  wire  is  held 
in  a  suitable  clamp,  it  may  set  itself  into  an 
angular  position  in  accordance  with  any 
electric  force  acting  on  the  pith  ball.  The 
wire  is  clamped  in  a  so-called  torsion  head 
at  the  upper  end  of  a  glass  tube.  By  means 
of  the  torsion  head  any  desirable  amount  of 
twist  can  be  given  to  the  upper  end  of  the 
wire  and  read  off  on  a  circular  scale,  whilst 
the  angular  position  assumed  by  the  beam  is 
indicated  on  a  second  scale  placed  at  the 
level  of  the  beam.  To  protect  the  apparatus 
from  air-currents  the  beam  is  enclosed  in  a 
cylindrical  glass  vessel.  In  making  experi- 
ments with  static  charges  it  is  important  to 
minimise  as  far  as  possible  dissipation  of  the 
charges  through  the  air,  and  for  this  reason 
precaution  should  be  taken  to  keep  the  air 
dry.  This  is  done  by  placing  into  the  glass 
vessel  a  saucer  with  chlorate  of  potassium. 
Any  moisture  originally  in  the  air  is  thereby 
extracted  and  rendered  harmless.  The  cover 
of  the  vessel  has  an  aperture  through  which 
is  lowered  a  second  gilded  pith  ball  so  as  just 
to  touch  that  on  the  scale  beam, 


ON  POTENTIAL  59 

If  now  an  electric  charge  is  imparted  to  the 
two  balls  by  touching  the  connecting  wire  of 
the  fixed  ball  with  a  charged  body,  the  beam 
is  deflected,  and  the  deflecting  force  can  be 
calculated  from  the  angular  position  at  which 
the  beam  comes  to  rest.  By  twisting  the 
torsion  head  the  balls  can  be  brought  nearer, 
and  a  new  position  of  equilibrium  obtained. 
Observations  of  the  deflection,  with  different 
amounts  of  twist  of  the  torsion  head,  are 
taken,  and  from  these  it  is  possible  to  calibrate 
the  balance,  that  is,  mark  out  the  scale,  and 
then  use  the  calibration  for  the  exact  measure- 
ment of  the  repulsive  forces  acting  between 
the  balls.  Coulomb  was  thus  able,  by  means 
of  his  torsion  balance,  to  establish  the  law  of 
electric  action  at  a  distance. 

We  may  look  on  the  torsion  balance  as  the 
practical  way  of  making  the  experiment 
described  in  Chapter  I.  There  is,  however, 
this  difference.  The  purely  experimental  part 
of  the  work  with  the  torsion  balance  is  quite 
simple,  and  free  from  external  disturbing 
influences,  but  the  mathematical  investiga- 
tion of  the  experimental  results  is  complicated. 
On  the  other  hand,  the  mathematics  of  the 
experiment  described  in  Chapter  I  are  quite 
simple  and  elementary,  but  the  practical  carry- 


60  ELECTRICITY 

ing  out  of  such  an  experiment  would  be  very 
difficult  and  costly.  As  I  am,  however,  not  con- 
cerned with  any  actual  experiment,  but  with 
the  explanation  of  first  principles,  I  prefer  to 
base  this  explanation  on  the  mathematically 
simple  but  technically  impracticable  experi- 
ment rather  than  on  an  experiment  which, 
although  easy  to  perform,  requires  a  com- 
plicated mathematical  interpretation. 

Let  us  then  revert  to  the  hypothetical 
experiment  of  a  large  electrified  sphere  sus- 
pended by  a  silk  thread  in  the  middle  of  a 
large  room.  Let  the  sphere  contain  a  charge 
of  Q  electrostatic  units  of  positive  electricity. 
Let  the  small  sphere  contain  unit  positive 
charge,  and  let  us  assume  that  we  may  place 
this  at,  and  measure  accurately  the  force  at, 
any  point.  We  shall  then  find  that  the 
general  law  of  action  through  space  holds 
good  if  we  measure  distances  between  the 
centres  of  the  spheres.  This  means  that  the 
distributed  charge  on  each  sphere  acts  as  if 
it  were  concentrated  in  its  centre,  a  fact  which 
can  also  be  proved  mathematically,  starting 
from  the  general  law.  The  repelling  force 
on  unit  charge  is  given  in  dynes  by  the 
expression 


ON  POTENTIAL  61 

This  force  diminishes  rapidly  as  we  increase 
the  distance;  at  10  times  the  distance  it  is 
_i_)  at  100  times  the  distance  it  is  I(>QOO  the 
original  value.  Obviously  if  the  room  is 
large  enough  it  may  be  practically  zero  close 
to  the  wall,  and  yet  quite  sensible  within  a 
foot  or  so  of  the  large  sphere. 

Let  us  assume  that  somehow  or  other  we 
pick  up  a  pith  ball  charged  with  unit  positive 
electricity  and  carry  it  along  any  path  to 
some  point  near  the  sphere.  All  the  way  we 
experience  a  repelling  force,  small  at  first,  but 
rapidly  increasing  as  we  approach  to  the  final 
position.  In  overcoming  this  repelling  force  we 
must  impress  mechanical  energy  on  the  pith 
ball,  and  the  energy  thus  stored  can  again  be 
recovered  in  letting  the  pith  ball  recede  and 
perform  mechanical  work  by  overcoming  some 
opposing  force,  so  regulated  that  it  balances  at 
any  point  the  repelling  force  of  electricity. 

We  need  not  concern  ourselves  with  the 
mechanism  by  which  such  a  process  could 
be  carried  out,  since  the  whole  experiment 
is  only  hypothetical  and  merely  intended  to 
illustrate  principles.  Our  unit  charge  then 
is  a  carrier  of  energy,  or  a  means  of  storing 
energy;  and  the  amount  of  energy  stored 
will  depend  on  the  charge  on  the  sphere, 


62  ELECTRICITY 

the  medium  in  which  the  approach  takes 
place,  and  the  distance  from  the  centre  of  the 
sphere  at  which  the  approach  is  arrested. 
Thus  to  every  point  of  space  surrounding 
the  sphere  corresponds  a  definite  amount  of 
energy.  The  nearer  the  point  is  to  the 
surface  of  the  sphere,  the  greater  is  the  amount 
of  energy  required  to  bring  unit  charge  to 
that  point.  By  moving  the  pith  ball  nearer 
to  the  sphere  we  must  expend  energy,  that  is, 
store  it ;  by  allowing  it  to  move  farther  away 
we  obtain  energy,  that  is,  we  diminish  the 
amount  stored.  If  we  move  the  pith  balJ 
round  the  sphere,  taking  care  to  keep  at  the 
same  distance,  we  neither  expend  nor  receive 
energy.  In  this  case  the  movement  takes 
place  everywhere  at  right  angles  to  the  direc- 
tion of  the  force,  and  consequently  no  work 
can  be  done.  Our  pith  ball  is  only  potent 
to  give  up  energy  if  allowed  to  recede  from 
the  sphere  in  obedience  to  its  repelling  force, 
and  the  measure  of  this  "  potency,"  or,  as 
we  may  shortly  term  it,  the  "  potential,"  is 
a  measure  of  the  total  energy  which  the  pith 
ball  yields  if  allowed  to  move  from  the  point 
in  question  to  a  point  so  far  away  that  the 
force  has  dwindled  to  zero — in  mathematical 
language,  to  a  point  infinitely  distant.  The 


ON  POTENTIAL  63 

potential  has  a  definite  value  for  every  point 
of  the  space  surrounding  the  charged  sphere. 
We  may  thus  define  it :  The  potential  at  any 
point  of  space  is  the  energy  required  to  bring  unit 
positive  charge  from  infinite  distance  to  that  point. 
We  have  yet  to  find  a  mathematical 
expression  for  the  potential.  To  do  so  we 
shall  assume  the  approach  to  the  sphere  to 
take  place  in  a  straight  line.  It  is  quite 
permissible  to  restrict  the  movement  to  this 
condition,  for  if  the  shape  of  the  path  made 
any  difference  to  the  energy  expended  on 
approach  and  recovered  on  recession,  we 
should  be  able  to  construct  a  perpetual 
motion  machine,  as  may  be  easily  seen  from 
the  following  consideration:  Imagine  that  a 
path  of  approach  could  be  found  which  required 
a  smaller  expenditure  of  energy  than  can  be 
recovered  if  the  pith  ball  is  constrained  to 
follow  on  its  outward  journey  some  other  path, 
then  we  could  by  a  suitable  sequence  of  the 
two  motions  create  energy.  We  know  that  the 
creation  of  energy  is  impossible,  and  we  must 
therefore  conclude  that  all  paths  are  equivalent 
as  far  as  the  potential  is  concerned.  We  are  thus 
justified  to  take  that  shape  of  path  which  lends 
itself  most  easily  to  a  mathematical  investiga- 
tion, and  that  is  the  straight  line. 


64,  ELECTRICITY 

Let  us  now  subdivide  the  straight  line,  along 
which  the  movement  takes  place,  into  a  very 
large  number  of  little  bits,  each  in  itself  so  small 
that  we  may  neglect  any  change  of  the  repelling 
force  within  the  two  ends  of  this  little  bit.  The 
force  varies  by  a  small  amount  from  bit  to 
bit,  but  within  the  limits  of  one  bit  or  small 
step  on  the  journey  we  consider  it  constant. 
Such  a  conception  is  quite  permissible  if  we 
take  the  steps  or  elements  of  the  path  small 
enough.  The  energy  corresponding  to  each 
elemental  part  of  the  journey  is  the  product 
of  the  length  of  the  element  divided  by  the 
square  of  the  distance  to  the  centre  of  the 
sphere,  and  multiplied  by  the  charge  on  it. 
To  each  step  thus  corresponds  a  little  bit  of 
the  total  energy,  and  by  adding  up  all  these 
little  bits  of  energy  we  get  the  potential.  It 
would  be  very  laborious  to  actually  map  out 
the  whole  of  the  journey  in  this  way  and  make 
the  innumerable  calculations  here  indicated. 
Fortunately  there  is  no  necessity  for  all  this 
arithmetical  work.  By  the  application  of  a 
mathematical  method  known  as  the  in- 
finitesimal calculus  we  are  able  to  arrive  at  the 
result  in  a  very  simple  way  by  one  operation. 
The  result  is  ^ 


ON  POTENTIAL  65 

where  V  is  the  potential  in  dyne-centimetres, 
Q  the  charge  on  the  sphere  in  electrostatic 
units,  and  D  the  distance  of  the  point  from 
the  centre  of  the  sphere  in  centimetres  at 
which  the  approaching  motion  has  terminated. 
The  reader  should  note  that  the  conception 
of  a  person  actually  carrying  a  body  containing 
unit  charge  in  his  hand,  and  approaching  it 
to  the  sphere,  is  merely  introduced  as  illus- 
trating a  mathematical  relation  between 
certain  quantities,  and  must  in  no  ways  be 
taken  literally.  The  formula  only  says  that 
the  potential  is  an  attribute  of  the  particular 
point  A  in  space  distant  D  cm.  from  the 
centre  of  the  active  mass  Q.  In  another 
point,  AJ  distant  Dj  cm.,  the  potential  will 
have  a  different  value,  say  Vr  If  A  is  nearer 
to  the  active  centre  than  A1,  then  V  will  be 
greater  than  V1?  and  we  may  therefore  speak 
of  a  potential  difference  V— Vl  existing  be- 
tween the  points  A  and  Ar  Or  in  symbols 


Since  D  is  smaller  than  D1?  the   potential 

difference  is  positive.   We  must  expend  energy 

in  bringing  the  unit  positive  charge,  and  in 

fact   any    positive   charge,    from   A1   to    A. 

E 


66  ELECTRICITY 

Conversely,  the  energy  thus  stored  can  be 
recovered  if  we  allow  the  unit  charge  to 
recede  from  A  to  A19  which  it  will  do  under 
the  repelling  force  from  the  active  mass  Q. 
Positive  electricity,  then,  tends  to  move 
from  the  point  of  higher  to  that  of  lower 
potential. 

This  is  self-evident ;  but  how  does  the  matter 
stand  if  the  sphere  is  charged  with  negative 
electricity  ?  We  have  then  not  repulsion, 
but  attraction  of  the  unit  charge.  The  force 
has  changed  sign.  The  potentials  at  A  and 
A!  are  both  negative,  but  that  at  A  is  more 
negative  than  that  at  Ar  Now  by  referring 
both  to  the  same  datum  line  we  may  also 
say  the  potential  at  A1  is  positive  as  com- 
pared to  that  at  A.  To  make  this  matter 
clear,  let  me  illustrate  by  substituting  height 
for  potential :  On  a  tableland  2000  ft.  above 
sea-level  there  is  a  mountain  500  ft.  high. 
At  the  foot  of  the  mountain  a  shaft  is  sunk 
500  ft.  deep. '  Referring  vertical  distances  to 
the  level  of  the  plain  we  say  the  level  of 
the  mountain-top  is  4-500  ft.  and  the  level 
of  the  bottom  of  the  mine-shaft  is  —  500  ft. ; 
but  if  we  refer  all  heights  to  the  sea-level 
we  would  give  the  mountain-top  as  +2500  ft. 
and  the  bottom  of  the  shaft  as  +1500  ft. 


ON  POTENTIAL  67 

Both  levels  (potentials)  are  positive,  but  the 
mountain  is  more  positive  than  the  mine. 

Let  us  now  revert  to  our  positively  charged 
sphere.  At  infinite  distance  the  potential 
is  zero,  and  as  we  approach  the  sphere  it 
becomes  positive  and  grows  in  value  inversely 
as  the  distance  diminishes.  Its  greatest 
possible  value  is  at  the  least  possible  distance, 
which  is  on  its  surface.  The  maximum  value, 
the  potential  of  the  sphere,  is  on  its  own  sur- 
face, and  is  numerically  given  by 


where  R  denotes  the  radius  of  the  sphere  in 
cm.  For  a  negatively  charged  sphere  the 
potential  at  infinite  distance  is  also  zero,  and 
on  its  surface  it  is 


A  unit  charge  free  to  move  will  therefore  fly 
from  infinity  towards  the  sphere  and  right  on 
to  it.  If  the  unit  charge  is  carried  on  some 
conductor  having  ponderable  mass,  this  con- 
ductor would  strike  the  surface  of  the  sphere 
with  a  certain  velocity.  It  is  easy  to  deter- 
mine this,  since  we  know  the  total  energy 
(namely,  the  potential  difference  between  in- 


68  ELECTRICITY 

finity  and  the  distance  R),  which,  during  the 
flight  of'  this  projectile,  has  been  stored  in 
it  in  the  shape  of  kinetic  energy.  By  a  well- 
known  law  of  mechanics  the  kinetic  energy 
stored  in  a  projectile  is  given  by  the  product 
of  half  its  mass  and  the  square  of  the  velocity. 
Since  the  mass  and  energy  are  known,  the 
velocity  can  be  calculated. 

Let  us  apply,  by  way  of  illustration,  this 
principle  of  equivalence  between  potential 
and  kinetic  energy  to  the  calculation  of  the 
velocity  with  which  a  meteorite  strikes  our 
earth.  The  potential  of  gravity  of  the  earth 
on  a  point  on  its  surface  is 

V-/M 
-  R 

where  M  is  the  mass  of  the  earth  and  R  its 
radius.  The  energy  stored  in  a  meteorite  of 
mass  m  is  therefore 


which  may  also  be  written  in  the  form 


But        ^  is  nothing  else  than   the   weight 
of  the  mass  m,  and  we  thus  find  that  the 


ON  POTENTIAL  69 

kinetic  energy  of  the  meteorite  is  the  product 
of  its  weight  multiplied  by  the  radius  of  the 
earth.  Adopting  the  engineer's  unit  of  energy 
as  the  metre-kilogram,  and  the  mass  unit 
as  that  mass  which  weighs  9-81  kg.,  we  must 
take  the  radius  of  the  earth  in  metres,  and  shall 
get  the  velocity  v  in  metres  per  second. 
Since  the  mass  of  our  meteorite  is  supposed 
to  be  unity,  we  have  the  equation 

E  =  9-81R 

from  which  we  find  fa2  =  9-81  x  636000 
v  =  11150 

The  meteorite  will  strike  the  earth  with  a 
velocity  of  11*15  kilometres  a  second;  in 
reality  a  little  less,  because  of  the  resistance 
of  the  air. 

This  digression  has  been  inserted  to  show 
the  application  of  the  potential  theory  to  a 
purely  mechanical  problem.  Let  us  now  re- 
turn to  the  electrical  aspect  of  this  theory. 
We  have  a  large  sphere,  charged  with  Q  units 
of  positive  electricity,  and  suspended  in  the 
middle  of  a  large  room.  The  potential 
difference  between  any  point  of  the  wall 
and  the  surface  of  the  sphere  is  numerically 
equal  to  the  energy  required  to  bring  a  unit 
of  positive  electricity  from  the  wall  to  the 


70  ELECTRICITY 

sphere.  The  wall  of  the  room  being  in 
contact  with  the  earth,  both  must  be  con- 
sidered as  at  the  same  potential,  and  if  we 
arbitrarily  fix  this  as  zero  (which  is  evidently 
permissible  since  we  deal  with  potential 
differences  and  may  take  our  datum  line  where 
we  like),  then  the  energy  expended  is  the  abso- 
lute potential  of  the  sphere.  We  may  also 
now  drop  the  conception  of  an  immensely 
large  room,  and  assume  the  sphere  suspended 
in  a  room  of  any  size,  or  even  in  the  open. 
This  does  not  mean  that  it  will  in  all  cases  be 
equally  easy  to  give  the  sphere  the  same 
charge  Q  irrespective  of  the  surroundings  ;  but 
it  means  that  for  the  same  charge  Q  the 
potential  on  the  surface  will  be  the  same 
whatever  the  surroundings  may  be.  Thus 
we  may  imagine  the  sphere  charged  in  the 
room  to  the  potential 


If  now  we  knock  down  the  walls,  or  carry 
the  sphere  into  another  room  or  into  the  open, 
there  will  be  no  change  in  its  potential  pro- 
vided that  we  can  avoid  loss  of  charge  by 
dispersion.  Now  how  are  we  to  give  the 
charge  Q  to  our  sphere?  We  cannot  pick 


ON  POTENTIAL  71 

up  positive  units  of  electricity  from  the 
ground  as  if  they  were  pebbles  and  carry 
them  by  hand  to  the  sphere ;  we  must  proceed 
in  a  different  way.  Let  us  then  take  a 
frictional  machine  and  connect  its  negative 
wire  to  the  ground,  and  the  positive  to  the 
sphere.  If  the  machine  is  worked,  it  will 
push  negative  electricity  into  the  ground  and 
positive  on  to  the  sphere.  In  other  words, 
a  charging  current  will  flow  along  that  wire, 
and  more  and  more  electricity  will  accumulate 
on  the  sphere  the  longer  the  machine  is  at 
work.  There  is,  however,  a  limit;  beyond 
which  the  process  of  charging  cannot  go.  At 
first,  it  is  easy  enough  to  push  electricity  on 
to  the  sphere,  because  there  is  only  a  little 
quantity  there  which  repels  the  influx  of  new 
units,  but  as  the  charge  proceeds  the  quantity 
accumulated  grows,  the  potential  grows,  and 
it  requires  more  and  more  energy  to  bring 
every  single  unit  on  to  the  sphere.  Finally, 
a  point  is  reached  when  the  pushing  force  of 
the  machine,  or,  as  we  term  it  technically, 
its  electromotive  force,  is  just  able  to  balance 
the  repelling  force  of  the  charge  accumulated, 
but  not  able  to  add  a  single  unit.  Thus  a 
state  of  equilibrium  is  reached,  and  the  charg- 
ing process  has  come  to  an  end.  If  we  want 


72  ELECTRICITY 

to  charge  still  a  little  more  electricity  on  the 
sphere,  we  must  increase  the  electromotive 
force,  or  e.m.f.  of  the  machine,  by  working 
it  quicker;  this  will  again  raise  the  potential, 
but  a  point  must  eventually  be  reached  when 
e.m.f.  and  potential  again  balance. 

We  have  thus,  as  the  limiting  condition  of 
the  process  of  charging,  equality  between 
potential  and  e.m.f.  It  may  be  objected  that 
this  statement  cannot  have  any  physical 
meaning,  because  we  are  comparing  two  things 
which  by  their  nature  are  different.  Potential 
is  of  the  nature  of  energy,  whereas  e.m.f.  is 
only  one  of  the  factors  which  make  up  energy. 
When  we  pay  our  electric  light  bill,  we  pay, 
really,  for  energy,  and  not  for  current  by 
itself;  nor  do  we  pay  for  e.m.f.  by  itself; 
nor  for  the  product  of  the  two.  What  we 
pay  for  is  the  product  of  three  things,  namely, 
current,  e.m.f.  and  time.  The  electricity 
metre,  which  says  how  much  we  have  to  pay, 
takes  account  of  all  three  factors,  and  gives 
the  energy  as  the  product  of  amperes,  volts, 
seconds,  or,  as  a  mere  matter  of  convenience, 
it  gives  it  in  kilovoltampere  hours,  the  unit 
legalised  by  Act  of  Parliament,  and  known 
as  the  "  Board  of  Trade  Unit  "  of  electrical 
energy.  As  a  matter  of  strict  logic  it  is  there- 


ON  POTENTIAL  73 

fore  not  permissible  to  equate  potential  and 
e.m.f.,  but  it  becomes  permissible  as  a 
numerical  proposition  the  moment  we  adopt 
such  a  unit  for  the  current,  that  the  product 
of  unit  current  and  unit  time  equals  unit 
charge  in  the  same  system  as  that  adopted 
in  expressing  the  charge  on  the  sphere.  Thus 
a  current  of  i  such  units,  flowing  for  t  seconds, 
corresponds  to  a  charge  of  q  units.  If  the 
electromotive  force  required  to  push  these  q 
units  on  to  the  sphere  is  denoted  by  e  units, 
then  the  energy  expended  is 

e  x  i  X  t  =  eq 

On  the  other  hand,  we  know  from  the  defini- 
tion of  the  potential  that  the  energy  required 
to  bring  q  units  from  the  wall  of  the  room  to 
the  sphere  requires  the  energy  V  q ;  and  hence 
it  is  evident  that  e  and  V  are  numerically 
equal.  By  adopting  the  system  of  units 
here  explained,  we  are  therefore  justified  in 
considering  e.m.f.  and  potential  as  numerically 
equal,  and  can  write 

e  =  ^         or         Q  =  eU 

The  charge  that  can  be  accumulated  on  a 
sphere  is  the  product  of  its  radius  and  the 
e.m.f.  developed  by  the  electric  machine. 
It  has  been  pointed  out  that  the  conception 


74  ELECTRICITY 

of  a  very  large  room,  in  which  the  sphere  is 
suspended,  is  not  necessary  to  our  arguments. 
We  may  reduce  the  room  to  any  extent,  and 
still  the  definition  of  potential,  or,  as  we 
now  see,  that  of  e.m.f.,  holds  good.  It  is 
the  energy  required  to  carry  unit  positive 
charge  from  the  wall  to  the  sphere.  Since 
there  is  no  restriction  to  the  size  of  the  room, 
other  than  there  must  not  be  actual  contact 
between  wall  and  sphere,  let  the  room  shrink 
until  it  has  become  merely  a  spherical  shell 
surrounding  the  sphere  closely,  the  distance 
being  a  very  small  length  d.  Let  this  be  a 
mere  clearance  space,  so  small  in  comparison 
with  the  radius  of  the  sphere  that  the  re- 
pelling force  of  the  charge  Q  on  our  unit  has 
sensibly  the  same  value  at  any  point  within 
this  very  narrow  space.  The  repelling  force  is 

Q 

R2 

and  since  the  product  of  force  and  distance 
traversed  is  energy,  we  find 


and 

R2 


instead  of  eR  as  found  previously,  when  the 


ON   POTENTIAL  75 

sphere  was  in  a  large  room  or  in  the  open. 
Comparing  now  the  two  cases,  namely,  the 
sphere  in  the  open  and  the  sphere  closely 
surrounded  by  a  metallic  envelope,  it  will  be 
seen  that  to  get  the  same  charge  on  the 
spheres  is  not  equally  easy.  The  sphere 
hanging  free  requires  the  application  of  a 
much  larger  e.m.f.  than  the  sphere  within  an 
envelope,  or,  to  put  it  another  way,  the  sphere 
with  an  envelope  will,  under  the  application 
of  the  same  e.m.f.,  acquire  a  much  greater 
charge  than  the  sphere  hanging  free  in  space. 
The  capacity  of  the  sphere  for  taking  a  charge 
has  been  increased.  This  reasoning  leads  us 
to  the  conception  of  capacity  as  a  property 
of  the  configuration  of  metallic  bodies.  We 
define  capacity  as  the  ratio  of  charge  divided 
by  e.m.f.  Using  the  symbol  C  for  capacity, 
the  definition  mathematically  expressed  is 


Since  we  found  previously  that  Q  =  eR,  it 
follows  that  the  capacity  of  a  sphere  in  the 
open  is  given  by  the  length  of  its  radius 
expressed  in  cm.  For  the  sphere  with  its 
envelope  the  capacity  is 


76  ELECTRICITY 

The  ratio  of  the  square  of  a  length  and  a 
length  is  again  a  length,  so  that  we  have  in 
both  cases  the  capacity  expressed  as  so  many 
cm. 

In  deducing  the  conception  of  capacity  we 
assumed  that  the  conductor  has  a  spherical 
shape,  but  obviously  if,  instead  of  suspending 
a  sphere  and  charging  it,  we  had  suspended 
a  metallic  body  of  any  shape  and  forced 
electricity  on  to  it  by  the  frictional  machine, 
it  would  have  acquired  some  charge  propor- 
tional to  the  e.m.f.  applied.  The  body  of 
irregular  shape  also  has  capacity,  only  we  may 
not  always  be  able  to  calculate  it  exactly 
beforehand.  It  can,  however,  always  be 
found  experimentally.  For  this  purpose  we 
apply  a  known  e.m.f.  to  charge  the  body  and 
then  discharge  it  through  a  special  kind  of 
measuring  instrument.  The  instrument  indi- 
cates the  quantity  of  charge  which  has  passed 
through  it ;  and  from  the  two  measurements, 
namely,  e.m.f.  and  quantity,  we  can  determine 
the  capacity.  For  certain  shapes  the  deter- 
mination of  capacity,  by  mathematical  reason- 
ing, is  quite  easy.  One  case,  namely  that  of 
the  sphere,  either  free  or  in  a  shell,  we  have 
already  treated.  The  case  of  concentric 
cylinders,  or  parallel  cylinders,  or  a  cylinder 


ON  POTENTIAL  77 

and  a  parallel  plane  is  also  easily  treated,  but 
it  would  exceed  the  limits  of  this  book  to 
enter  into  such  details,  which  have  more 
immediate  interest  for  the  cable  engineer  or 
the  telegraphist.  The  case  of  two  parallel 
plates  may,  however,  be  here  given,  because 
the  derivation  of  a  mathematical  expression 
for  the  capacity  is  exceedingly  simple.  We 
found  that  the  capacity  of  concentric  spheres 
is  given  by  the  expression 


If  we  multiply  nominator  and  denominator 
with  4tjt  we  do  not  alter  the  equation,  so  that 
we  also  may  write 


4?rR2  is  nothing  else  than  the  surface  of  the 
sphere,  so  that  we  also  have 

C-   S 

~*7ld 

The  capacity  is  therefore  given  by  the  surface 
divided  by  4nd.  The  radius  does  no  longer 
appear  in  our  formula.  If  we  assume  the 
radius  to  be  infinitely  large,  any  part  S  of 
the  surface  becomes  a  plane,  and  we  thus  have 
for  the  capacity  of  two  parallel  plane  surfaces 


78  ELECTRICITY 

of  S  square  cm.,  distant  d  cm.,  the  expression 

C-    S 

~ 


which  is  again  a  length. 

Bodies  constructed  for  holding  an  electric 
charge,  that  is,  intended  to  condense  electricity 
on  their  surfaces,  are  technically  termed  con- 
densers. The  first  condenser  used  by  physic- 
ists was  the  so-called  "  Leyden  Jar  "  acci- 
dentally discovered  by  Musschenbroek  (1692- 
1761),  Professor  of  Physics  in  Leyden,  Holland. 
In  the  eighteenth  century  electricity  was 
considered  a  "  fluid,"  and  Musschenbroek 
attempted  to  collect  some  of  this  fluid  in  a 
glass  filled  with  water.  He  held  the  glass  in 
the  hand,  and  electrified  the  water  by  a  wire 
placed  in  the  glass  and  projecting  sufficiently 
far  out  so  that  he  could  touch  the  conductor 
of  his  frictional  machine  with  the  wire.  When 
removing  the  glass  and  taking  out  the  wire,  he 
received  an  electric  shock  much  more  violent 
than  he  could  obtain  from  his  machine  directly. 
In  this  case  the  water  formed  the  inner  con- 
ductor and  the  hand  the  outer  shell,  whilst  the 
space  between  the  two  was  filled  by  glass. 

This  form  of  condenser  has  become  known 
under  the  name  of  Leyden  Jar,  and  is 
used  to  this  day  by  physicists.  It  consists 


ON  POTENTIAL  79 

of  a  glass  jar  coated  on  the  inner  and  outer 
surface  with  tinfoil  about  half-way  up.  The 
uncoated  part  of  the  jar  is  varnished  to 
minimise  loss  of  charge  along  the  surface  of 
the  glass.  An  improved  form  of  Leyden  jar 
has  been  designed  by  Mr.  Mosicki,  and  is 
largely  used  in  wireless  telegraphy.  The 
coating  of  tinfoil  is  replaced  by  silvering,  and 
the  shape  of  the  glass  vessel  is  designed  with 
special  reference  to  its  ability  to  withstand 
very  high  e.m.f.'s.  Whereas  the  ordinary  jar 
of  the  physical  laboratory  can  only  be  used 
with  an  e.m.f.  of  about  20,000  volts,  the 
Mosicki  condenser,  as  made  for  wireless  tele- 
graph stations,  can  be  used  up  to  an  e.m.f.  of 
60,000  volts.  Mosicki  condensers  are  also 
used  for  the  protection  of  electric  power  lines 
from  atmospheric  electricity,  and  from  the 
effects  of  sudden  electric  disturbances.  They 
act  as  a  kind  of  electric  buffer  or  elastic  link, 
able  to  soften  the  blow  which  the  line  and 
machinery  might  otherwise  receive  with  full 
force  if  there  were,  from  any  cause,  a  sudden 
increase  in  the  charge  on  the  system. 

When  the  condenser  is  not  subjected  to  a 
very  high  potential  difference,  the  insulator 
separating  its  two  surfaces  or  coatings  need 
not  be  glass,  but  may  be  a  cheaper  material, 


80  ELECTRICITY 

such  as  paraffined  paper.  The  object  of  using 
some  lining  between  the  plates  is  twofold. 
In  the  first  place  it  would  be  technically  very 
difficult  to  insure  a  very  small  intervening 
space  without  the  risk  that  the  plates  come 
actually  into  contact.  If  the  condenser  is 
not  required  to  have  a  large  capacity,  and 
especially  if  it  is  to  be  used  as  a  standard  of 
capacity  for  comparison  with  other  conden- 
sers, then  the  intervening  space  between  the 
plates  may  be  left  without  filling  material. 
Such  condensers  are  called  "  air  condensers." 
Where  a  condenser  of  larger  capacity  is 
required  as  a  standard,  then  the  filling-in 
material,  the  so-called  "  dielectric,"  may  be 
mica.  This,  even  in  thin  sheets,  is  electrically 
very  strong,  and  is  also  an  excellent  insulator. 
It  is  thus  possible  to  make  the  space  between 
the  plates  very  small,  and  by  this  means 
obtain  a  larger  capacity  with  a  given  plate 
surface  than  with  an  air  condenser.  The 
other  reason  for  using  another  material  than 
air  as  a  dielectric  is  that  the  material  by  itself 
has  the  property  of  increasing  the  capacity. 
We  have  seen  in  Chapter  I  that  the  attrac- 
tive force  depends  on  the  medium  between  the 
two  charged  surfaces.  If  this  medium  is  air, 
the  force  is  greatest ;  if  it  is  an  insulator  such 


ON  POTENTIAL  81 

as  oil,  glass,  mica  or  paper,  it  is  K  times 
smaller.  This  means  that  to  bring  a  unit  of 
positive  charge  to  our  sphere  through  such  a 
medium  takes  K  times  less  energy  than  to 
bring  it  through  air.  In  other  words,  to 
obtain  the  same  charge  an  e.m.f.  K  times 
smaller  is  sufficient,  or,  if  the  e.m.f.  is  the  same, 
the  resulting  charge  will  be  K  times  larger. 
Hence  by  using  a  dielectric  other  than  air 
the  capacity  of  our  condenser  is  increased  K 
times.  The  following  table  gives  the  value 
of  K  for  some  dielectric  materials — 

VALUES  OF  THE  SPECIFIC  INDUCTIVE  CAPACITY 
K  IN  THE  C.G.S.  ELECTROSTATIC  SYSTEM 

Material  .....         K 

Glass 2-10 

Mica 5-6 

Insulating  Oil  used  in  transformers  .       2-1 
Paraffin  Wax  ....       2-3 

India  Rubber  ....   2-2-2-8 

Gutta  Percha  ....   2-5-4 

Paper,  as  used  for  power  cables        .   2-6-3-5 
Paper,  as  used  in  telephone  cables      .      2-2-5 
Paper,    paraffined,    as   used    in    con- 
densers      .         .          .          .          .7-2 
Distilled  Water        ....      76 

Pure  Alcohol 26 

F 


82  ELECTRICITY 

Li  the  old  method  of  making  condensers 
with  paper  as  a  dielectric  the  coatings  or 
"  electrodes  "  were  sheets  of  tinfoil,  but  in  the 
modern  type  of  condenser  developed  by  Mr. 
Mansbridge,  of  the  British  Post  Office,  so- 
called  metallised  paper  is  used  interleaved 
with  plain  paper,  both  being  paraffined.  The 
effect  of  this  improvement  is  that  the  bulk, 
weight  and  cost  of  paper  condensers  have  been 
reduced  to  less  than  one  tenth  of  what  they 
were  formerly.  The  capacity  of  any  con- 
denser is  given  in  electrostatic  c.g.s.  units  by 
the  formula 

r  —  K"  ^ 

\~>  —  XV  ~: « 

4>Jio 

This  unit  is  inconveniently  small,  and  for 
practical  work  a  much  larger  unit,  namely,  the 
"  microfarad,"  has  been  adopted.  As  the 
name  implies,  the  microfarad  is  the  one 
millionth  part  of  the  farad,  and  the  mag- 
nitude of  the  farad  is  given  by  the  following 
definition  :  A  condenser  of  one  farad  capacity, 
when  charged  under  the  e.m.f.  of  one  volt, 
will  store  that  quantity  of  electricity  which 
is  represented  by  the  flow  of  one  ampere 
during  one  second.  The  ratio  of  the  electro- 
static unit  of  capacity  to  the  microfarad 
is  1  to  9  x  105,  so  that  the  capacity  of  a 


ON   POTENTIAL  83 

condenser  expressed  in  microfarads  is  given 
by  the  formula 

™       K     S 
M=113     7 

where  S  is  the  surface  of  the  dielectric  in 
square  metres,  6  is  the  thickness  of  the 
dielectric  in  millimetres,  and  K  has  the  value 
given  in  the  above  table. 

In  developing  the  theory  of  the  potential 
we  started  with  the  experiment  of  bringing 
unit  electricity  from  the  wall  of  the  room  to  a 
point  outside  the  charged  sphere;  and,  as  a 
limiting  condition,  to  its  surface.  Beyond 
that  we  did  not  go.  But  what  happens  if  we 
pass  the  surface  and  carry  our  unit  through 
to  the  inside  ?  A  mathematical  investigation 
shows  that  in  this  case  no  force  at  all  is  acting 
on  the  unit  charge,  and  in  fact  on  any  body 
carrying  a  charge  of  any  magnitude.  Since 
in  moving  such  a  body  about  within  the 
hollow  sphere  we  experience  no  resisting 
force  whatever,  no  energy  is  required  to  per- 
form the  motion,  and  consequently  all  points 
of  the  interior  space  must  have  the  same 
potential.  Any  point  of  the  inner  surface 
of  the  sphere  is  a  point  in  the  interior,  but 

since  the  surface  has  the  potential  j|  it  follows 


84  ELECTRICITY 

that  this  is  also  the  potential  right  through 
the  cavity  of  the  hollow  sphere.  This  law 
that  the  potential  at  any  point  inside  a  con- 
ductor is  the  same  as  the  potential  on  its 
surface,  may  also  be  proved  without  the  aid 
of  mathematics  by  the  following  reasoning: 
Imagine  a  conductor  of  any  shape,  and  assume 
it  at  first  to  be  solid  right  through.  No  free 
electricity  could  possibly  remain  in  the 
substance  of  the  metal,  since  the  mutual 
repulsion  of  all  the  elementary  charges  would 
cause  these  to  try  to  move  apart  as  far  as  they 
can.  As  the  carrier  of  these  charges  is 
metallic,  that  is  to  say,  offers  no  resistance 
to  the  free  displacement  or  flow  of  electricity, 
there  is  nothing  to  hinder  the  movement,  and 
consequently  the  charge  will  all  accumulate 
on  the  outside  surface.  There  is,  therefore,  no 
charge  in  the  body  of  the  metal,  and  we  may, 
without  changing  the  electrical  condition, 
take  away  the  inside  and  leave  only  the 
merest  shell,  and  still  there  can  be  no  electrical 
effect  produced  inside  the  shell.  We  may 
charge  such  a  shell  with  the  strongest  machine 
made,  and  yet  in  the  inside  not  a  trace  of 
electricity  can  be  detected. 

This  has  first  been  proved  experimentally 
by  Faraday,  who  constructed  for  the  purpose 


ON  POTENTIAL  85 

a  large  cage  of  wire  gauze  and  went  into  it 
armed  with  the  most  delicate  instrument  for 
the  detection  of  electric  charges.  The  cage  was 
placed  on  insulating  supports  and  strongly 
electrified  by  a  frictional  machine.  Not  a 
trace  of  electrification  could  be  detected  in  the 
interior  or  the  inner  surface  of  the  wire  gauze. 
The  principle  of  the  "  Faraday  Cage  "  has  been 
applied  as  a  protective  device  in  various  ways. 
Professor  Artemieff ,  of  the  Moscow  University, 
has  constructed  an  electrical  safety  dress, 
which  completely  envelopes  the  wearer  so 
that  he  is  literally  enclosed  in  a  tight-fitting 
Faraday  Cage.  The  dress  is  of  metal  gauze, 
and  as  long  as  the  surface  is  continuous,  the 
wearer  is  absolutely  safe  from  shock.  If  a 
discharge  flash  from  a  high-tension  apparatus 
should  strike  him,  the  charge  flows  through 
the  dress  to  earth  without  doing  any  damage. 
Another  important  application  of  the  same 
principle  is  the  protection  of  underground  or 
submarine  cables.  The  part  of  the  cable  that 
is  below  the  ground  or  the  sea  is  naturally 
protected  against  lightning  strokes,  but  some- 
where the  end  of  the  cable  must  be  brought 
out  to  the  surface  of  the  earth  and  connected 
to  some  apparatus  or  machine.  At  that  point 
both  the  end  of  the  cable  and  the  machinery 


86  ELECTRICITY 

are  liable  to  be  struck  and  must  be  protected. 
The  best  possible  protection  is  to  place  the 
whole  of  the  machinery  and  the  apparatus 
connected  to  the  cable  into  an  iron  house. 
It  is  not  necessary  that  the  walls  of  the  house 
be  entirely  made  of  iron.  In  Milan  there  is 
such  a  house  for  the  protection  of  the  junction 
of  the  overhead  power  lines  coming  from  the 
Alps,  and  joining  by  means  of  certain  appa- 
ratus with  the  underground  cable  network 
that  supplies  the  town  with  electricity.  In 
appearance  this  house  is  not  different  from 
any  of  the  other  factory  buildings  of  the 
neighbourhood;  nevertheless  it  is  a  Faraday 
Cage.  The  roof  has  an  iron  lining,  the  stan- 
chions are  well  bonded  with  it  and  with  each 
other,  and  go  down  to  the  moist  subsoil. 
Below  the  plastering  of  the  walls  is  a  heavy 
expanded  metal  lining  all  connected  to  the 
~oof  and  stanchions,  and  the  windows  have 
*ron  frames  also  in  good  electrical  connection 
with  the  metal  walls.  The  building  thus 
forms  a  metal  shell,  and  affords  complete 
protection  to  its  contents  against  any  electrical 
disturbance  from  outside. 


CHAPTER  IV 

ELECTRIFICATION   BY  MECHANICAL  MEANS 

IT  has  been  shown  in  the  last  chapter  that 
potential  may  be  considered  as  an  attribute 
of  space  produced  by  the  presence  of  a  charged 
conductor.  In  every  point  of  the  space 
surrounding  such  a  conductor,  there  acts  a 
force  pushing  positive  electricity  one  way  and 
negative  electricity  the  opposite  way.  If  the 
charged  body  is  positively  electrified,  the 
potential  will  be  positive  all  around  it,  but 
higher  close  to  the  body  and  lower  the  farther 
we  recede  from  it.  We  must  conceive  a  charge 
as  a  something  which  is  adhering  to  a  con- 
ducting surface;  where  there  is  no  conductor 
there  can  be  no  charge,  though  there  may  be 
potential.  Now  the  very  definition  of  a 
conductor  is  a  body  over  the  surface  of  which 
electricity  can  distribute  itself  without  hin- 
drance, that  is  to  say,  only  under  the  influence 
of  the  potential  force  that  pushes  it.  The 
region  of  space  surrounding  the  charged  body 
8.7 


88  ELECTRICITY 

in  which  the  potential  has  a  sensible  value  is 
called  the  "  electric  field."  A  unit  charge 
brought  into  any  point  of  this  field  will 
experience  a  force  acting  in  a  certain  direction ; 
in  the  case  of  the  field  being  due  to  the 
presence  of  a  charged  sphere  the  force  acts 
either  radially  outward  from  or  radially 
inward  to  the  centre  of  the  sphere.  Where 
the  conductor  is  of  a  more  complicated  shape, 
or  where  it  is  surrounded  by  a  conducting 
surface  kept  at  a  different  potential,  for 
instance,  earth  potential  or  zero,  there  also 
corresponds  to  each  point  of  the  electric  field 
a  particular  direction,  and  obviously  one 
direction  only,  along  which  the  force  acts. 
A  unit  positive  charge,  liberated  in  any  point 
of  the  field,  will  follow  the  impulse  of  that 
force  and  move  from  point  to  point  along  a 
particular  line,  and  we  may  thus  speak  of  a 
"  line  of  force,"  meaning  thereby  the  path 
along  which  a  unit  charge,  or  in  fact  any 
charge  of  positive  electricity,  is  urged. 

This  conception  of  lines  of  force,  as  char- 
acterising the  qualities  of  an  electric  field,  is 
due  to  Faraday.  Thus  far  lines  of  force  merely 
have  a  geometrical  significance,  namely,  that 
of  the  direction  of  the  electric  force,  but  it 
is  easy  to  see  that  they  must  also  have  a 


ELECTRIFICATION  89 

dynamic  significance.  Obviously  if  we  move 
along  a  line  of  force,  the  actual  magnitude  of 
the  mechanical  force  experienced  by  the  unit 
charge  does  not  necessarily  remain  the  same. 
Take  the  simple  case  of  the  field  due  to  a 
charged  sphere  hanging  free  in  space.  The 
lines  of  force  are  all  straight  lines  converging 
to  the  centre  of  the  sphere.  If  at  a  distance 
of  one  yard  our  unit  charge  is  repelled  with 
a  certain  force,  then  at  a  distance  of  half  a 
yard  the  force  would  be  quadrupled.  Thus, 
although  we  may  travel  along  one  and  the 
same  line  of  force,  the  magnitude  of  the  force 
changes  inversely  as  the  square  of  the  distance. 
As  we  approach  the  sphere,  the  potential 
increases  inversely  as  the  first  power  (not  the 
square)  of  the  distance.  Potential  and  force 
are  two  things  of  different  character,  namely, 
energy  and  mechanical  force  respectively. 
We  have  seen  that  potential  may  be  con- 
sidered as  an  attribute  of  space,  and  the  idea 
lies  near  to  also  consider  electric  force  as 
an  attribute  of  space,  although  as  an  attribute 
of  a  different  character.  This  attribute  is  a 
mechanical  force,  namely,  the  force  exerted  on 
unit  positive  charge. 

Let  us  see  how  we  could  make  a  mechanical 
model  of  the  lines  of  force  emanating  from  a 


90  ELECTRICITY 

charged  sphere.  We  might  represent  each 
liiie  by  a  straight  wire  stuck  into  the  surface 
of  the  sphere  and  pointing  true  to  the  centre. 
We  should  thus  get  a  kind  of  spherical  hedge- 
hog ;  to  represent  a  strong  field  due  to  a  large 
charge  we  should  stick  into  the  sphere  more 
wires,  and  to  represent  a  weak  charge  we 
should  use  a  smaller  number  of  wires,  but  in 
all  cases  the  wires  would  be  evenly  distributed 
all  over  the  sphere.  An  imaginary  sphere, 
laid  round  the  nucleus  from  which  all  the 
wires  spring,  will  be  pierced  by  all  the  wires 
whatever  may  be  the  radius  of  this  imaginary 
sphere,  but  the  number  of  wires  piercing  a 
unit  of  the  surface  of  the  imaginary  sphere 
will  be  inversely  proportional  to  the  square 
of  its  radius.  But  we  know  that  the  force 
is  also  proportional  to  the  inverse  square  of 
the  distance  from  the  centre.  The  two  things 
follow  the  same  law,  and  it  is  therefore  obvious 
that  by  a  suitable  selection  of  units  we  may 
express  the  force  at  any  point  by  a  number 
indicating  how  many  wires  pierce  a  unit  of 
the  surface  of  the  imaginary  sphere  laid 
through  the  point.  Thus  the  density  of  the 
lines  of  force  passing  through  the  surface  at 
the  point  in  question  is  a  measure  of  the 
mechanical  force  exerted  on  unit  charge  at 


ELECTRIFICATION  91 

that  point.  This  is  the  dynamic  significance 
of  the  conception  of  lines  of  force  introduced 
by  Faraday.  The  density,  or  number  of  lines 
to  the  unit  surface  is  called  the  electric 
"  induction,"  and  the  force  experienced  by 
unit  charge  is,  then,  simply  equal  to  the 
induction,  whilst  the  mechanical  force  ex- 
perienced by  a  body  charged  with  q  units 
will  be  q  times  as  great.  Writing  the  symbol 
B  for  the  induction,  the  force  is  given  by  the 
formula 

F  =B  x  q 

B  may  be  considered  as  of  the  nature  of  a 
flow  of  force,  or  "  flux,"  piercing  each  square 
centimetre  of  the  imaginary  sphere  laid 
through  the  point  in  question,  and  the  total 
flux  emanating  from  the  charged  nucleus  will 
then  be  represented  by  the  product  of  B  and 
the  total  surface  of  the  imaginary  sphere  laid 
round  it.  .  It  will  also  in  our  mechanical  model 
be  represented  by  the  total  number  of  wires 
we  have  stuck  into  this  nucleus.  But  the 
total  number  is  the  same  whatever  be  the 
radius  of  the  imaginary  sphere.  To  get  the 
relation  between  original  charge  Q  on  the 
nucleus  and  total  flow  of  force  emanating 
from  it,  we  may  therefore  choose  any  radius. 


92  ELECTRICITY 

By  adopting  a  radius  equal  to  unity  we  get 
for  the  surface  the  expression  4<n,  and  for  the 
total  flux  the  expression  0  =  4>7iB.  We 
know  that  the  force  on  unit  pole  at  unit 

O  x  1 

distance  is  —  2—  =  Q.     We  also  know  that 

the  force  is  B  x  1  =  B,  from  which  it  follows 
that  B  and  Q  are  numerically  equal,  and 
hence  we  find  as  an  expression  for  the  total 
flux  emanating  from  Q  units  of  electric  charge 


The  conception  of  lines  of  force  is  very  useful 
in  forming  a  mental  picture  of  the  properties  of 
an  electric  field  by  mechanical  analogy,  but  the 
analogy  must  not  be  taken  in  too  literal  a 
sense.  We  must  not  think  of  lines  of  force 
in  the  same  way  as  we  think  of  the  stalks 
of  corn  in  a  field,  namely,  as  physical  lines 
each  bound  to  a  definite  position.  In  adopting 
such  a  view  we  would  be  met  at  once  by  the 
difficulty  that  our  unit  charge,  being  placed 
midway  between  two  lines  of  force,  would  not 
experience  any  force.  This  is  contrary  to 
experiment;  we  cannot  find  any  place  in  a 
field  of  sensible  magnitude  where  the  force 
acting  on  unit  charge  is  zero.  To  escape  the 
difficulty  some  writers  use  the  expression 


ELECTRIFICATION  93 


"  tube  of  force "  instead  of  line  of  force, 
thereby  indicating  that  the  force  is  not  limited 
to  a  particular  mathematical  line,  but  acts 
with  equal  strength  in  any  point  of  the  same 
transverse  section  of  the  tube. 

Let  us  now  apply  the  conception  of  lines,  or 
tubes  of  force,  to  see  what  must  happen  if  a 
non -charged  conductor  is  approached  to  a 
charged  conductor.  In  Fig.  2  the  circle  on 


FIG.  2. 

the  right  represents  a  sphere  charged  with 
positive  electricity.  On  the  left  is  a  cylinder 
with  rounded  ends  containing  no  charge 
originally.  Each  tube  of  force  emanating 
from  the  charged  sphere  has  the  property  of 
pulling  negative  electricity  towards  the  sphere 
and  pushing  positive  electricity  as  far  away 
from  it  as  possible.  These  forces  produce  a 
separation  of  the  two  electricities  originally 
combined  on  the  non -charged  cylinder,  so  that 


94  ELECTRICITY 


a/»rkm*» 


the  end  pointing  to  the  sphere  will  become 
negatively  and  the  other  end  positively 
electrified.  The  question  is,  how  strongly  ? 
Obviously  it  is  a  matter  of  conflicting  forces. 
The  left  end  of  the  cylinder  contains  positive 
and  the  right  end  negative  electricity.  If 
the  sphere  were  taken  away,  the  attraction 
between  the  two  charges  would  cause  them 
immediately  to  flow  together,  and,  neutralising 
each  other,  the  cylinder  would  again  appear 
uncharged,  as  it  was  before  we  approached 
it  to  the  sphere.  There  is  thus  a  separating 
force  due  to  the  sphere,  and  a  uniting  force  due 
to  the  mutual  action  of  the  two  ends  acting 
simultaneously,  and  the  result  is  that  the 
quantity  of  charge  which  can  be  accumulated 
on  each  end  of  the  cylinder  is  not  unlimited. 
Now  let  us  touch  the  cylinder  with  the 
finger.  The  negative  charge  has  no  desire  to 
flow  away  through  our  body  to  earth,  for  it  is 
attracted  by  the  charge  of  the  sphere,  but  the 
positive  charge  of  the  cylinder  is  pushed  away 
by  the  action  of  the  tubes  of  force  and  will 
flow  as  far  as  it  can.  Before  the  cylinder  was 
touched  it  went  to  the  farthest  point,  namely, 
the  left-hand  end  of  the  cylinder,  but  the 
moment  we  touch  it  we  give  it  a  path  to  flow 
much  farther,  namely,  through  our  body  to 


ELECTRIFICATION  95 

earth,  that  is,  right  away  to  zero  potential. 
We  have  thus  brought  the  potential  of  the 
cylinder  to  zero,  and  increased  the  potential 
difference  between  sphere  and  cylinder.  We 
have  strengthened  the  tubes  of  force  passing 
from  sphere  to  cylinder.  The  total  flux 
emanating  from  the  sphere  has  not  altered, 
for  that  is  strictly  limited  by  the  charge 
originally  on  the  sphere,  but  whilst  with  a 
sphere  free  in  space  the  flux  is  evenly  dis- 
tributed all  round,  we  have,  by  bringing  the 
cylinder  near,  and  especially  by  discharging 
its  positive  electricity  to  earth,  disturbed  the 
symmetrical  field  of  the  sphere,  making  it 
much  denser  on  its  left  half,  and  thus  increased 
the  inductive  effect  on  the  cylinder.  The  charge 
at  its  left  end  will  be  increased.  If  we  now 
interrupt  the  connection  to  earth,  we  have  a 
negatively  charged  cylinder,  and  we  may  carry 
this  charge  to  some  third  conductor,  and  by 
touching  it  with  the  cylinder  impart  to  it  a 
negative  charge .  This  process  may  be  repeated. 
Approach  the  cylinder  to  the  sphere  again, 
discharge  the  cylinder  to  earth,  then  pick  it  up 
by  its  insulating  stand  and  carry  it  again  into 
contact  with  the  third  conductor  and  so  on. 

By  this  process    the  third   conductor   be- 
comes   negatively   charged  without  the  use 


96  ELECTRICITY 

of  a  frictional  machine  or  voltaic  battery. 
The  third  conductor,  then,  becomes  the 
nucleus  of  an  electric  field,  and  as  we  know 
that  an  electric  field  cannot  be  produced 
without  the  expenditure  of  energy,  the  ques- 
tion arises  where  that  energy  comes  from. 
A  moment's  consideration  will  show  that  the 
energy  is  given  by  our  hand  in  carrying 
the  cylinder  to  and  fro.  Whilst  approach- 
ing the  uncharged,  or  weakly  negatively 
charged,  cylinder  to  the  sphere  we  receive 
energy.  There  is  attraction,  because  the 
negative  end  which  is  attracted  is  always 
nearer  than  the  positive  end  which  is  repelled. 
After  the  cylinder  has  been  discharged  to 
earth  '  there  remains  only  attraction,  and 
against  this  attractive  force  the  cylinder  has 
to  be  pulled  away.  Here  our  hand  is  called 
upon  to  impart  energy  to  the  system.  We 
electrify  the  third  conductor  by  the  expendi- 
ture of  energy,  that  is,  by  mechanical  means. 
The  more  often  we  carry  the  cylinder  to  and 
fro,  the  more  negative  electricity  do  we 
accumulate  on  the  third  conductor,  but  it  is 
evident  that  this  process  cannot  go  on  for 
ever.  We  are  only  able  to  accumulate  a 
definite  charge  on  the  third  conductor.  As 
this  becomes  charged,  its  tube  of  force  also 


ELECTRIFICATION  97 

develops  and  finally  becomes  as  strong  as 
those  of  the  sphere.  Then  the  third  conductor 
refuses  to  take  any  of  the  negative  charge  of 
the  cylinder,  and  the  process  of  accumulation 
ceases.  If  we  wish  it  to  go  on  further  we 
must  increase  the  source  from  which  the 
negative  charge  of  the  cylinder  is  derived, 
that  is,  we  must  charge  the  sphere  more 
strongly.  How  are  we  to  increase  this 
positive  charge  ?  The  most  obvious  thing  is 
to  increase  it  also  by  mechanical  means,  much 
in  the  same  way  as  we  increase  the  charge  on 
the  third  conductor,  and  this  is  the  principle 
on  which  the  modern  electric  machines,  the 
so-called  "  influence  machines,"  work. 

The  process  is  not  carried  out  in  the 
primitive  manner  here  explained  merely  by 
way  of  elucidating  a  principle,  but  still  the 
essential  feature  is  retained  of  a  go-between, 
or  carrier  of  small  charges,  between  the  two 
conductors  on  which  the  electricities  of 
opposite  sign  are  to  be  accumulated.  A 
familiar  example  of  a  practica^  way  of  making 
use  of  this  principle  is  the  electrophorus,  but 
I  shall  not  discuss  it  here,  as  it  may  be 
found  in  any  elementary  textbook.  I  prefer 
to  deal  at  once  with  apparatus  in  which  the 
principle  of  accumulating  action  is  carried  on 


98 


ELECTRICITY 


automatically.     It  is  only  apparatus  of  this 
kind  which  has  practical  importance. 

As  an  example  of  a  very  simple  kind  of 
automatic  apparatus  we  may  take  Lord 
Kelvin's  "  water -dropping  machine."  Let, 


FIG.  3. 

in  Fig.  3,  A  and  B  be  two  metal  cylinders 
supported  on  insulating  stands,  and  a  and 
b  two  metal  funnels  likewise  supported.  A 
and  a  are  connected  by  a  wire;  B  and  b  are 
similarly  connected.  To  indicate  that  the 
two  connecting  wires  at  the  crossing  point  in 


ELECTRIFICATION  99 

the  drawing  do  not  touch,  one  is  shown  as 
going  round  it  in  a  little  half-circle.  This 
is  the  usual  method  used  in  electrical  diagrams 
of  showing  that  two  wires  cross  without 
touching.  Owing  to  the  metallic  connection 
established  by  these  wires,  the  potential  of 
A  is  always  the  same  as  the  potential  of  a. 
Similarly  B  and  b  are  at  the  same  potential. 
Into  the  middle  of  each  cylinder  there  is  carried 
the  discharge  nozzle  of  a  water  pipe,  and  the 
flow  of  water  is  regulated  by  means  of  a  stop- 
cock in  such  manner  that  there  shall  be  no 
continuous  stream,  but  a  succession  of  drops. 
The  drawing  is  only  diagrammatic,  and 
does  not  represent  the  actual  shape  of  the 
parts.  In  conductors  intended  for  the  accumu- 
lation of  a  charge,  all  sharp  corners  must  be 
avoided  so  as  to  minimise  dispersion  of  charge, 
which  is  strongest  the  smaller  the  radius  of 
curvature.  Any  corner  is  in  reality  a  curved 
surface,  but  with  a  very  small  radius  of 
curvature.  The  different  parts  of  a  charge 
distributed  over  any  surface  repel  each  other. 
If  the  surface  is  quite  plane  the  repelling  force 
between  the  elementary  particles  of  the  charge 
is  parallel  to  the  surface,  and  there  is  no  com- 
ponent tending  to  flake  electricity  off  the 
surface  and  disperse  it  into  the  air.  If  the 


100  ELECTRICITY 

surface  is  curved  there  is  such  a  component, 
and  it  becomes  the  greater  the  more  sharply 
the  surface  is  curved.  At  a  sharp  corner  it 
becomes  very  great,  and  if  the  corner  is  drawn 
out  into  a  sharp  point  the  force  is  so  great  that 
all  the  charge  is  dissipated  as  soon  as  brought 
to  the  conductor.  Hence  lightning-rods,  wh  ich 
are  intended  to  dissipate  any  charge  which 
may  be  induced  in  a  building  by  a  charged 
cloud  overhead  as  quickly  as  possible,  and  so 
avert  the  threatened  stroke,  are  provided 
with  sharp  points.  The  gilding  is  not  essen- 
tial, but  more  in  the  nature  of  an  extravagant 
refinement.  The  only  excuse  one  can  find  for 
such  a  refinement  is  that  gilding  protects  the 
iron  from  rusting,  and  so  preserves  the  sharp- 
ness of  the  point.  In  the  water-drop] >ing 
machine  we  would,  of  course,  also  avoid  the 
sharp  corners  by  making  the  outside  of  each 
part  more  or  less  spherical,  without,  however, 
altering  the  inner  and  essential  parts. 

The  connection  between  Figs.  2  and  3  will 
be  obvious  at  a  glance.  The  cylinder  A  corre- 
sponds to  the  charged  sphere,  and  the  drop 
of  water  hanging  from  the  end  of  the  pipe 
corresponds  to  the  right-hand  end  of  the 
cylinder.  It  becomes  negatively  electrified 
by  induction,  and  on  falling  carries  this 


ELECTRIFICATION 

negative  charge  to  the  funnel  b.  This  pro- 
duces a  small  increase  in  the  negative  charge 
on  the  inducing  cylinder  B.  The  drops  of 
water  falling  through  B  are  positively  electri- 
fied, and  on  striking  the  funnel  a  give  up  their 
charge  to  it,  which  accession  of  charge  is 
conveyed  to  the  inducing  cylinder  A,  making 
it  more  efficient  for  charging  the  drops  of 
water  which  pass  through  its  interior.  We 
have  thus  a  cumulative  action  between  the 
inducing  cylinders,  the  drops  of  water  and  the 
collecting  funnels.  The  limit  of  this  cumu- 
lative process  is  reached  when  the  dispersion 
of  charge,  due  to  the  growing  potential  differ- 
ence, just  balances  the  accession  of  charge 
carried  by  the  drops  of  water  from  one  in- 
ducing cylinder  to  the  other.  We  have  here 
a  case  of  electrification  by  mechanical  means, 
namely,  the  motion  of  drops  of  water.  The 
energy  represented  by  the  electric  field  be- 
tween A  and  B  is  derived  from  falling  water. 
The  use  of  water  in  an  apparatus  for  pro- 
ducing electrification  is  not  always  convenient, 
and  under  certain  circumstances,  as,  for  in- 
stance, on  board,  ship,  quite  impossible, 
because  in  a  sea-way  the  drops  would  not  fall 
plumb  into  the  collecting  funnels.  But  it  is 
precisely  in  submarine  telegraphy  generally, 


ELECTRICITY 

and  also  in  the  process  of  laying  submarine 
cables,  that  some  apparatus  for  producing 
strong  electrification  is  required.  This  need 
arises  in  connection  with  a  receiving  instru- 
ment known  as  the  syphon  recorder.  If  a 
permanent  record  of  the  telegraphic  message 
is  desired,  the  receiving  apparatus  itself  must 
write  down  this  message,  not  in  actual  letters, 
but  in  certain  telegraphic  code  signs  on  a 
moving  strip  of  paper.  To  use  a  pen  in  touch 
with  the  paper  is  out  of  the  question,  because 
the  mechanical  force  exerted  by  the  mechan- 
ism of  the  receiving  telegraph  instrument  is, 
with  the  feeble  electric  currents  that  can  be 
got  to  pass  through  a  submarine  cable,  too 
small  to  overcome  the  friction  between  paper 
and  pen.  In  order  to  allow  the  pen  to  move 
unfettered  and  write  freely  it  must  not  touch 
the  paper.  This  is  done  by  using  for  a  pen  a 
capillary  glass  tube  and  electrifying  the  ink. 
We  have  then  a  conductor,  namely,  the  ink, 
with  a  fairly  sharp  point,  namely,  the  capillary 
end  of  the  tube.  It  was  shown  above  that  the 
force  which  causes  electricity  to  flake  off  from 
a  conductor  is  very  great  at  a  sharp  point,  and 
thus  the  electricity  dispersing  from  the  end  of 
the  tube  takes  the  ink  with  it,  thus  squirting 
it  against  the  paper.  In  this  manner  the  slight 


ELECTRIFICATION  103 

and  unfettered  movements  of  the  pen  are  re- 
corded on  the  paper  without  the  pen  touching  it. 
The  problem,  therefore,  is  to  keep  the  ink 
electrified  notwithstanding  that  some  of  the 
charge  is  continuously  dissipated  in  the  action 
of  squirting  the  ink  on  to  the  paper.  It  is 
necessary  to  replenish  the  charge,  and  the 
apparatus  for  this  purpose,  which  is  also 


FIG.  4. 

the  invention  of  Lord  Kelvin,  is  called  the 
"  replenisher."  The  apparatus  gives  the 
original  charge  and  replenishes  it  from  time 
to  time.  All  the  telegraph  operator  has  to 
do  is  to  twist  a  knob  quickly.  Fig.  4  is  a  dia- 
grammatic representation  of  the  essential  parts 
of  Lord  Kelvin's  replenisher.  A  and  B  are  two 
segments  of  a  metallic  cylinder,  insulated 
from  each  other  and  connected  respectively 


104  ELECTRICITY 

to  the  two  conductors  g  and  /,  between  which 
a  difference  of  potential  is  to  be  established 
or  kept  up — in  our  case  ink  and  paper. 
Within  the  cylindrical  cavity  is  another  pair 
of  insulated  segments  a  and  6,  connected  by  an 
insulating  bridge-piece  C  mounted  on  a  spindle, 
by  which  the  inner  system  may  be  revolved. 
The  knob  above  mentioned  is  fixed  to  the  end 
of  this  spindle.  By  twirling  the  knob  rapid 
rotation  of  the  two  inner  segments  can  be 
produced,  and  thus  a  is  alternately  brought  to 
face  A  and  B  at  the  same  times  that  b  is 
brought  to  face  B  and  A  respectively.  The 
inner  segments  have  each  a  projecting  piece 
by  which  a  momentary  connection  is  estab- 
lished with  fine  wire  brushes.  These  are  fixed 
in  the  position  shown  d,  e,  /,  g.  The  brushes 
d  and  e  are  connected  by  a  wire,  and  the  other 
two  brushes  are  connected  as  shown  with  the 
outer  segments. 

To  explain  the  action  of  the  replenisher,  let 
us  start  with  the  assumption  that  A  has  a 
small  positive  and  B  a  small  negative  charge. 
It  is  immaterial  how  small  these  charges  are, 
since,  as  will  be  seen  presently,  the  action  is 
cumulative,  so  that  the  merest  trace  of  a  charge 
quickly  grows  to  a  quite  formidable  value.  It 
may  be  here  mentioned  that  the  same  principle 


ELECTRIFICATION  105 

is  utilised  in  the  well-known  electric  gas- 
lighters,  where  the  whole  of  the  mechanism 
diagrammatically  represented  in  the  sketch 
Fig.  4  is  contained  in  the  handle  of  the  instru- 
ment. The  rotation  is  produced  by  pressing  a 
knob,  and  the  cumulative  action  is  vigorous 
enough  to  raise  the  potential  of  the  two  outer 
segments  to  sparking-point.  The  spark  is 
produced  at  the  end  of  a  tube,  which  is  held 
over  the  issuing  gas-jet. 

Let  us  then  assume  that  there  is  a  very 
feeble  charge  on  A  and  B.  If  A  is  positive,  a 
will  receive  a  very  small  negative  charge  and 
b  a  very  small  positive  charge.  Let  the  rota- 
tion be  clockwise.  As  the  inner  segments 
advance,  the  contact  at  the  brushes  is  broken, 
and  the  negative  charge  of  a  is  carried  towards 
B.  When  the  inner  segment  a  has  made  a 
quarter  turn,  its  contact  piece  touches  the 
brush  /,  and  thus  the  feeble  charge  is  given 
up  to  B,  making  its  charge  just  a  little  stronger 
than  it  was  at  starting.  At  the  same  time  the 
feeble  charge  on  b,  which  is  positive,  is  given  up 
to  A,  making  also  that  charge  a  little  stronger 
than  it  was.  After  half  a  turn  from  the  start 
the  segments  a  and  b  have  changed  places. 
They  are  again  in  contact  by  the  brushes  d 
e,  and  b  acquires  now  a  negative  and  a  a  positive 


106  ELECTRICITY 

charge  which  they  carry  forward  and  give  up 
to  B  and  A  respectively,  again  increasing  the 
original  charge.  Thus  at  each  half  revolution 
of  the  internal  carrier  the  charges  on  the  outer 
segments  are  increased,  the  process  being 
cumulative,  but  also  in  this  case  limited  by 
the  dispersion  of  electricity,  which,  with  an 
increasing  potential  difference,  eventually 
reaches  so  high  a  value  that  the  charge  brought 
in  each  half  revolution  by  the  carrier  just 
balances  the  leakage  of  electricity  during 
the  time  it  takes  to  perform  the  half  revolu- 
tion. The  faster  we  twirl  the  knob,  the  shorter 
is  this  time,  and  the  smaller  the  leakage  per 
half  revolution.  By  twirling  faster  a  higher 
potential  between  the  outer  segments  can  be 
attained.  This  means  in  the  electric  gas- 
lighter  a  more  vigorous  and  effective  spark. 
When  it  is  required  to  accumulate  large 
charges  and  to  produce  spark  discharges  of 
considerable  magnitude,  machines  on  a  larger 
scale  must  be  used.  These  are  known  under 
the  name  of  "  influence  machines."  Such 
machines  have  been  constructed  by  Toepler, 
Holtz,  Voss  and  others,  but  the  type  most 
commonly  used  in  England  is  that  designed  by 
Wimshurst,  of  which  Fig.  5  is  a  diagrammatic 
representation.  Two  discs  of  highly  insulating 


ELECTRIFICATION 


107 


material,  such  as  ebonite  or  varnished  glass, 
are  set  co-axially  very  close  together,  and 
supported  on  horizontal  spindles  which  have 
opposite  direction  of  rotation.  Each  disc  has 
pasted  on  the  outside  a  large  number  of 
segments  of  tinfoil.  On  each  side  of  the 


FIG.  5. 

pair  of  discs  there  is  fixed  a  metal  bar  dia- 
metrically across,  and  provided  at  its  two 
ends  with  fine  wire  brushes  just  touching 
the  row  of  sectors  as  they  sweep  by  when 
the  disc  revolves.  These  two  metal  bars  are 
set  with  an  inclination  of  about  45  degrees 
to  the  horizontal,  but  not  in  the  same  direc- 
tion, so  that  the  angle  they  include  is  about 


108  ELECTRICITY 

90  degrees.  The  angular  setting  of  the  bars 
may  be  altered  between  about  60  and  90 
degrees,  so  as  to  get  the  most  efficient  condi- 
tion of  working.  In  addition  to  the  two  bars 
with  their  four  brushes,  there  are  the  two 
devices  for  collecting  the  electricities  of 
opposite  sign.  Each  consists  of  a  U-shaped 
rod,  the  limbs  of  the  U  embracing  the  pair 
of  discs  from  the  outside  and  being  provided 
with  a  "  comb  "  of  sharp  points  before  which 
the  sectors  pass.  The  collecting  combs  are 
set  on  a  horizontal  line.  The  direction  of 
rotation  of  each  disc  is  such  that  a  particular 
sector,  having  just  passed  a  comb,  turns 
through  an  acute  angle  in  order  to  reach  the 
brush  on  the  cross  bar  on  the  same  side. 

Fig.  5  is  a  diagrammatic  representation  of 
the  Wimshurst  machine,  but  for  the  sake  of 
greater  clearness  I  have  substituted  con- 
centric cylinders  for  the  parallel  discs.  The 
direction  of  rotation  is  shown  by  the  arrows. 
Let  the  inner  cylinder  represent  the  front 
disc,  and  the  outer  the  disc  at  the  back.  The 
discs  themselves  are  not  shown,  only  the  seg- 
ments which  are  represented  by  the  short 
lines.  The  cross  bar  for  the  front  disc  is 
shown  by  a  straight  line,  that  for  the  back  disc 
by  a  curved  line.  This  is  done  merely  to 


ELECTRIFICATION  109 

avoid  lines  crossing  each  other  and  thus 
rendering  the  diagram  less  clear.  Electrically, 
a  curved  conductor  is  as  good  as  a  straight 
one.  The  collecting  devices  are  represented 
by  the  two  pairs  of  points  facing  the  segments 
on  a  horizontal  diameter:  The  conductors 
in  which  the  charges  are  accumulated  are 
shown  by  the  circles  into  which  a  plus  and 
minus  sign  is  inscribed. 

To  explain  the  action  of  the  machine,  let 
us  assume  that  by  some  means  a  very  slight 
difference  of  potential  has  been  imparted  to 
two  opposite  segments  of  the  outer  cylinder, 
say  to  the  segments  A  and  B.  This  may  be 
done  by  approaching  a  rubbed  stick  of  sealing- 
wax,  but  generally  such  a  difference  of  potential 
exists  naturally.  We  cannot  walk  across  a 
dry  carpet,  or  run  the  hand  along  a  piece  of 
furniture,  without  producing  some  slight 
electrification  which  has  the  effect  of  setting 
up  potential  differences  between  different 
points  of  space,  and,  as  the  merest  trace  of 
such  a  potential  difference  suffices  to  start 
the  cumulative  process,  machines  of  the 
Wimshurst  type  generally  start  without 'the 
necessity  of  previous  electrical  excitation. 
It  suffices  to  turn  the  handle  and  so  cause  the 
discs  to  rotate  in  the  proper  sense.  Let  us 


110  ELECTRICITY 

then  assume  that  the  potential  of  the  segment 
A  is  a  little  higher  than  that  of  segment  B; 
in  other  words,  that  A  has  a  very  slight 
positive  and  B  an  equally  slight  negative 
charge.  The  cross  bar  with  the  segments 
a  b  is  at  that  moment  very  much  in  the  same 
condition  as  the  cylinder  in  Fig.  2,  that  is  to 
say,  the  end  pointing  to  the  positive  segment 
A  (which  takes  the  place  of  the  sphere  in 
Fig.  2)  becomes  by  induction  the  place  where 
a  negative  charge  collects,  and  the  end  b 
the  place  where  a  positive  charge  collects, 
only  the  induction  is  augmented  because  B 
also  influences  the  induced  system  in  the  same 
sense.  As  the  inner  cylinder  revolves,  a 
moves  to  the  right  and  is  detached  from  the 
brush  on  the  cross  bar,  and  takes  its  charge 
with  it.  The  same  happens  with  the  segment 
b,  which  takes  its  positive  charge  to  the  left. 
The  segments  a  and  b  eventually  arrive  in 
the  positions  c  and  d  respectively.  In  this 
position  they  come  opposite  to  two  outer 
segments  C  and  D.  The  roles  are  now  re- 
versed ;  it  is  the  charge  on  the  inner  segment 
which  produces  a  displacement  of  electricity 
along  the  cross  bars  connecting  C  and  D, 
and  the  charges  on  these  segments  are  carried 
on  as  the  outer  cylinder  rotates,  C  moving 


ELECTRIFICATION  111 

to  the  left  into  the  position  previously 
occupied  by  A,  and  D  moves  to  the  right  into 
the  position  previously  occupied  by  B.  But 
the  charge  on  C  is  of  the  same  sign  as  that  with 
which  A  started  the  process,  and  will  therefore 
act  in  the  same  sense,  only  more  strongly, 
since  it  has  been  reinforced  by  the  inductive 
action  just  explained.  Thus  during  rotation 
of  the  two  rows  of  segments  in  opposite 
sense  the  original  very  slight  electrification  is 
rapidly  increased,  and  a  considerable  quantity 
of  electricity  may  be  taken  off  by  the  action 
of  the  collecting  combs  and  accumulated  on 
the  electrodes.  It  will  be  observed  that  the 
segments  of  both  discs,  whilst  passing  each 
other  on  the  horizontal  diameter,  are  charged 
with  electricity  of  the  same  sign,  namely, 
positive  on  the  left  and  negative  on  the  right. 
If  we  now  inquire  as  to  the  true  cause  of 
electrification,  we  find  that  apart  from  the 
quite  insignificant  initial  charge  on  A  and  B, 
it  is  simply  the  mechanical  energy  required 
to  produce  rotation  against  the  opposing 
force  of  electrostatic  attraction  between  the 
outer  and  inner  segments.  A  has  a  positive, 
and  a  has  a  negative  charge.  These  two 
segments  therefore  attract  each  other;  as  a 
moves  to  the  right  and  A  to  the  left,  they  are 


112  ELECTRICITY 

pulled  apart  against  this  attractive  force,  and 
energy  is  therefore  required  to  produce  this 
motion.  It  is  this  energy  which,  by  the  action 
of  the  machine,  is  converted  into  the  potential 
energy  represented  by  the  electric  field  sur- 
rounding the  two  electrodes.  To  increase  the 
charge  it  is  customary  to  connect  the  elec- 
trodes with  the  knobs  of  two  Ley  den  jars, 
since  by  the  use  of  a  condenser  the  quantity 
of  electricity,  which  can  be  accumulated  with 
a  given  difference  of  potential,  is  greatly 
augmented.  That  energy  is  used  in  producing 
electrification  is  distinctly  felt  when  working 
the  machine  by  hand.  The  machine  gets 
charged  after  a  few  turns  of  the  handle,  and 
the  operator  feels  that,  as  the  charging  pro- 
gresses, it  gets  harder  to  turn  the  handle. 
In  large  machines  the  manual  work  becomes 
so  heavy  that  it  is  convenient  to  use  an 
electric  motor  for  working  the  machine. 


CHAPTER  V 

THE   ELECTRIC   CURRENT 

IN  Chapter  II  use  has  already  been  made  of 
the  term  electric  current.  The  term  meant  the 
transfer  of  a  positive  charge  through  a  wire 
from  a  point  where  the  potential  is  higher  to 
one  where  the  potential  is  lower.  Observa- 
tion shows  that  the  quantity  which  can  be 
transferred  in  unit  time  depends  not  only 
on  the  difference  of  potential,  but  also  on  the 
material  and  the  cross  section  of  the  wire. 
A  stout  wire  will  transfer  a  bigger  quantity 
in  unit  time  than  a  thin  wire,  or,  as  we  may 
also  say,  it  is  able  to  carry  a  bigger  current. 
When  it  is  a  question  of  electricity  in  motion 
the  conductor  must  have  body,  whilst  as  we 
have  seen,  with  electricity  at  rest  only  the 
surface  counts,  or,  to  speak  more  correctly, 
only  the  capacity  counts.  But  the  capacity 
of  a  sphere  in  space,  or  of  a  Leyden  jar,  is 
quite  independent  of  the  thickness  of  the  metal 
parts.  A  wooden  sphere  covered  with  the 
thinnest  layer  of  gold-beater's  skin  will  at  the 
H  113 


114  ELECTRICITY 

same  potential  hold  exactly  the  same  quantity 
of  electricity  as  if  it  were  made  of  solid  brass 
or  lead  or  any  other  metal.  Electricity  at 
rest  resides  entirely  on  the  outside  of  a  metal 
conductor.  We  might  reduce  the  thickness 
of  a  shell  to  any  degree,  and  still  the  charge 
is  not  altered. 

Now  let  us  follow  this  fact  to  its  logical  con- 
clusion. What  will  happen  if  we  reduce  the 
thickness  of  the  shell  to  zero  ?  If  thickness  has 
nothing  to  do  with  the  capacity,  then  by  redu- 
cing it  to  nothing  at  all  we  should  not  alter  the 
capacity.  In  other  words,  the  body  which  holds 
a  charge  need  not  be  a  conductor  at  all.  Its 
conducting  property  is  only  necessary  to  let  the 
charge  distribute  itself  over  the  whole  of  its 
surface,  in  fact  to  get  a  charge  on  to  it  at  all. 
If,  however,  the  charge  is  not  transferred  to 
the  surface  from  outside,  but  actually  produced 
on  the  surface,  then  there  is  no  need  that  the 
surface  should  be  the  surface  of  a  conductor. 
This  will  be  clearly  seen  if  we  reflect  that  a 
glass  rod,  although  a  very  good  insulator, 
may  be  electrified  by  rubbing.  Its  insulating 
property  is  a  positive  advantage,  since  we 
may  hold  one  end  in  our  hand  and  yet  electrify 
the  surface  at  the  other  end.  The  charge 
is  not  able  to  slip  about  freely  over  the  whole 


THE  ELECTRIC  CURRENT       115 

surface,  as  is  the  case  with  a  charged  con- 
ductor ;  hence,  if  we  touch  a  particular  point 
of  the  electrified  part,  we  take  off  a  little  of 
the  charge  at  that  point,  but  the  rest  of  the  rod 
remains  charged.  We  thus  see  that  a  charge 
can  reside  on  the  surface  of  an  insulator,  and 
it  can  be  proved  experimentally  that  the 
charge  even  penetrates  a  little  way  into  the 
body  of  the  insulator. 

If  a  Leyden  jar  or  a  paper  condenser  be 
discharged  and  left  standing  a  little  while,  a 
second  though  very  much  weaker  discharge 
may  be  taken  from  it.  It  is  as  though  the 
electricity  had  soaked  into  the  body  of  the 
dielectric  and  some  of  it  was  thus  prevented 
from  getting  out  at  the  first  discharge.  When 
the  jar  has  apparently  been  completely  dis- 
charged, there  is  still  left  a  small  residual 
charge,  which  slowly  leaks  out  on  to  the 
surface  of  the  glass  and  is  then  ready  to 
produce  a  second  discharge  spark.  If  the 
dielectric  is  mica,  this  phenomenon  of  soaking 
is  much  less  pronounced,  and  if  air  is  used  as 
a  dielectric,  it  is  absent. 

A  very  striking  experiment  may  be  made  to 
show  that  the  charge  in  a  Leyden  jar  does  not 
reside  on  the  surface  of  the  metal  coatings,  but 
on  the  surface  of  the  glass.  Imagine  a  metal 


116  ELECTRICITY 

beaker  into  which  fits  a  glass  beaker  and  into 
that  a  second  metal  beaker.  The  latter  may 
have  a  stem  and  discharge  knob  much  in  the 
same  way  as  an  ordinary  Leyden  jar,  the  only 
difference  being  that  the  inner  and  outer 
coatings  are  not  pasted  on  to  the  glass,  but 
are  removable.  If,  after  charging  this  jar, 
we  take  out  the  inner  metal  beaker  by  insu- 
lated tongs,  and  also  remove  the  glass  beaker 
from  its  outer  envelope,  we  have  completely 
dissected  the  jar.  The  two  metal  coatings 
may  be  handled,  the  glass  may  be  picked  up 
by  the  hand  touching  the  outside,  and  yet  when 
we  put  the  Leyden  jar  together  again,  we 
find  that  it  still  contains  the  original  charge, 
less  a  certain  unavoidable  leakage,  since  no 
insulator  is  perfect.  We  thus  see  that  any 
body,  whether  insulator  or  conductor,  may 
hold  a  static  charge  on  its  surface. 

Why  then  do  we  make  the  electrodes  of  an 
electric  machine,  such  as  that  diagrammatically 
represented  by  Fig.  5,  of  brass  and  not  of  glass  ? 
For  the  simple  reason  that  a  glass  electrode, 
although  quite  capable  of  holding  a  charge,  is 
very  ill-adapted  for  receiving  it.  The  charge 
must  be  conveyed  to  it  by  a  wire,  and  from 
the  point  where  the  wire  joins  it  the  charge 
must  be  able  to  flow  to  all  points  of  the  surface. 


THE  ELECTRIC  CURRENT      117 

This  flow  is  impossible  through  the  body  of  the 
glass,  since  glass  is  an  insulator.  Conversely, 
if  we  touch  a  charged  glass  sphere  at  one 
point  we  may  take  off  a  little  of  the  charge, 
but  not  the  whole  of  it,  which  is  distributed 
over  the  sphere.  Between  electricity  at  rest 
and  in  motion,  or  as  we  may  also  say,  between 
static  charges  and  currents,  there  is  thus  the 
fundamental  distinction  that  the  static  charge 
requires  surface  and  the  moving  charge  body. 

The  greater  the  current  we  wish  to  convey, 
the  stouter  must  be  the  wire.  The  com- 
mercial unit  of  current  is  the  Ampere,  so 
named  after  the  great  French  physicist.  We 
may  define  the  current  existing  in  a  particular 
point  of  the  wire  as  the  number  of  unit  charges 
which  pass  that  point  during  one  second. 
The  magnitude  of  the  electrostatic  unit 
of  quantity  has  been  defined  in  Chapter  I, 
p.  13.  By  experiment  it  has  been  proved 
that  one  ampere  is  represented  by  the  passage 
of  3000  millions  of  such  units  per  second. 

Man  has  no  sense  by  which  he  can  estimate 
the  strength  of  a  current  flowing  in  a  wire — 
by  touching'  the  wire  he  may  get  a  shock  and 
thus  conclude  that  the  wire  is  at  a  higher 
potential  than  he  is  himself  when  standing 
on  the  earth ;  and  indeed  wiremen,  who  have 


118  ELECTRICITY 

grown  reckless  in  their  calling,  often  resort 
to  this  simple  test  to  find  out  whether  a  wire 
is  what  is  technically  termed  "  alive,"  but 
no  amount  of  shocks  will  ever  enable  a  man 
to  say  how  many  amperes  are  flowing  in  the 
wire.  This  can  only  be  determined  by 
observation  of  certain  effects  produced  by  the 
current.  These  effects  may  be  chemical, 
thermal,  magnetic  or  mechanical. 

Chemical  action  of  an  electric  current. — The 
substance  of  a  copper  wire  carrying  a  current 
undergoes  no  change.  It  may  get  heated 
whilst  the  current  flows,  but  chemically  it 
remains  unaltered.  Even  if  the  wire  is  an 
alloy  of  two  metals  there  is  no  change  in 
its  chemical  nature.  Also  with  liquid  con- 
ductors, such  as  mercury  or  molten  iron,  the 
passage  of  a  current  does  not  produce  a 
chemical  change,  but  if  the  liquid  is  some 
chemical  compound  there  is  such  a  change. 
Imagine  two  copper  plates  placed  in  a  solution 
of  copper  sulphate  and  provided  with  terminals 
AB,  such  as  shown  in  Fig.  1,  p.  48.  Attach 
to  these  terminals  the  wires  leading  to  a 
dynamo  machine  or  some  other  source  from 
which  an  electric  current  flowing  always  in 
the  same  direction  may  be  obtained.  Let  us 
also  put  into  the  circuit  some  instrument 


THE  ELECTRIC  CURRENT       119 

which  will  record  the  total  quantity  of 
electricity  that  has  passed  through  the  solution 
in  a  given  time,  such  as  a  recording  electricity 
meter  used  in  the  sale  of  electricity  to  house- 
holders. We  shall  find  that  the  copper  plate 
at  which  the  current  enters  gets  gradually 
thinner,  and  that  at  which  the  current  issues 
gradually  stouter  exactly  in  the  same  measure, 
showing  that  the  current  has  the  effect  of  trans- 
porting copper  from  the  one  plate  to  the  other. 
An  arrangement  of  this  kind  is  called  an 
electrolytic  cell,  and  the  process  going  on  in 
the  cell  is  called  electrolysis.  The  plates  are 
called  the  electrodes,  and  the  liquid  between 
them  is  the  electrolyte.  The  electrode  by 
which  the  current  enters  is  also  called  the 
anode,  and  that  by  which  it  leaves  is  called 
the  kathode.  The  current  flows  from  the 
anode  into  the  electrolyte  and  from  the 
electrolyte  to  the  kathode,  taking  the  copper 
with  it.  If  instead  of  copper  sulphate  the 
electrolyte  contained  some  other  metallic 
salt,  the  current  would  split  this  up  chemically 
and  take  the  metal,  whatever  it  may  be,  with 
it  and  deposit  it  on  the  kathode.  This  is 
the  principle  on  which  objects  are  silver-  OP 
nickel-plated.  It  is  also  the  principle  on 
which  copper  is  refined  on  a  large  scale.  The 


120 


ELECTRICITY 


anode  is  a  block  of  impure  copper,  and  is 
gradually  dissolved  by  the  passage  of  the 
current.  The  dissolved  copper  goes  into  the 
solution,  and  out  of  this  only  the  pure  copper 
is  transported  by  the  current  and  deposited 


FIG.  6. 

on  the  kathode,  the  impurities  falling  to  the 
bottom  of  the  cell  as  a  sludge. 

The  reader  may  ask,  what  happens  if  we 
use  as  metal  for  the  electrodes  platinum  which 
resists  chemical  action  ?  In  this  case  the 
electrodes  act  simply  as  collectors  for  the 
substances  which  are  being  extracted  out  of 
the  electrolyte  by  the  current.  Let  us  take 


THE  ELECTRIC  CURRENT       121 

the  simplest  case  of  the  electrolyte  being 
water,  which  has  been  rendered  conducting 
by  a  slight  addition  of  some  chemical,  such 
as  sulphuric  acid.  The  two  substances  out 
of  which  water  is  formed  are  the  gases  oxygen 
and  hydrogen.  The  current,  in  passing 
through  the  water,  tears  these  oxygen  and 
hydrogen  atoms  asunder  and  carries  them  off, 
the  hydrogen  in  the  direction  of  its  own  flow, 
namely,  to  the  kathode,  and  the  oxygen  in  the 
opposite  direction,  that  is  to  say,  to  the  anode. 
Here  the  gases  are  deposited  in  the  form  of 
bubbles,  which  from  time  to  time  become 
detached  and  rise  to  the  surface.  By  using 
an  arrangement  such  as  shown  in  Fig.  6 
the  gases  may  be  separately  collected  and 
their  volume  measured.  A  and  K  are  two 
platinum  wires  fused  into  the  bottom  of  the 
glass  vessel,  which  is  filled  with  acidulated 
water.  Over  these  electrodes  are  placed  two 
inverted  glass  tubes  also  filled  with  'water  and 
closed  at  the  top,  so  that  the  gases  liberated 
at  the  electrodes  may  be  collected  and  their 
volume  measured.  It  is  found  that  the  space 
filled  by  hydrogen,  H,  is  exactly  twice  as 
great  as  that  filled  by  oxygen,  O ;  and  this  is 
precisely  the  volumetric  proportion  in  which 
these  two  gases  form  water.  The  direction 


122  ELECTRICITY 

of  the  current  is  shown  by  the  arrow.  There 
is  a  migration  of  hydrogen  atoms  in  the 
direction  of  the  arrow  through  the  liquid, 
and  a  migration  of  oxygen  atoms  in  the 
opposite  direction.  We  actually  see  the 
bubbles  forming  on  the  kathode  and  anode, 
yet  we  see  no  bubbles  passing  through  the 
liquid.  The  formation  of  bubbles  shows  that 
there  is  actually  a  tearing  apart  of  the  two 
gases  close  to  the  surface  of  the  electrodes,  but 
apparently  there  is  no  such  tearing  apart  in  the 
body  of  the  liquid,  for  we  see  no  bubbles  there. 
This  apparent  anomaly  has  been  cleared 
up  on  the  basis  of  an  hypothesis  by  Grotthus, 
which  may  be  put  in  homely  language 
by  reference  to  a  ball-room.  Let  each  male 
dancer  stand  for  an  oxygen  atom  and  each 
woman  for  a  hydrogen  atom.  Let  the  room 
be  crowded,  and  all  the  dancers  be  properly 
paired.  A  man  looking  down  on  the  throng 
sees  only  couples,  but  no  single  persons. 
Now  suppose  that  by  some  rule  of  the  dance, 
at  a  given  signal  one  man  at  one  end  of  the 
room  must  leave  his  partner  and  cling  to  the 
wall,  whilst  at  the  same  moment  a  woman  at 
the  other  end  of  the  room  must  do  the 
same.  This  will  disturb  the  homogeneity  of 
the  throng,  but  that  can  immediately  be 


THE  ELECTRIC  CURRENT       123 

restored  if  all  the  couples  in  a  direct  line 
between  the  two  walls  change  partners  and 
thus  absorb  the  two  partnerless  persons  again 
into  the  general  dancing  throng.  Our  ob- 
server on  the  gallery  would  then  not  notice 
any  difference  in  the  assembly;  all  remain 
properly  paired. 

The  electrolysis  of  water  is  commercially 
utilised  for  the  production  of  pure  oxygen 
and  hydrogen.  The  electrodes  are  of  iron, 
and  the  electrolyte  is  a  16%  soda  solution. 
The  cost  of  the  process,  including  cost  of 
power,  labour,  interest  and  depreciation, 
varies  from  9d.  to  Is.  2d.  per  one  cubic  meter 
oxygen  +  two  cubic  meters  hydrogen,  accord- 
ing to  the  magnitude  of  the  plant  and  local 
conditions. 

Electrolysis  is  not  confined  to  liquids;  it 
can  also  be  produced  in  a  solid,  provided  it  is  a 
conductor.  Thus,  if  a  current  is  sent  through 
a  lump  of  caustic  potash,  it  is  decomposed  into 
oxygen  and  the  metal  potassium.  Let,  in 
Fig.  7,  P  be  a  platinum  plate,  C  a  lump  of 
caustic  potash,  and  M  a  globule  of  mercury 
placed  into  a  cavity  hollowed  out  of  the  solid 
electrolyte ;  then,  on  the  passage  of  a  current 
in  the  direction  shown  by  the  arrows,  oxygen 
will  collect  on  the  surface  of  the  platinum,  and 


124  ELECTRICITY 

potassium  will  collect  on  the  under  surface 
of  the  mercury,  forming  with  it  an  amalgam. 
By  distilling  off  the  mercury  under  exclusion 
of  the  air,  the  metal  potassium  may  be  obtained 
in  a  free  state.  In  this  way  Davey  first 
succeeded  in  producing  free  potassium  and 
sodium;  in  fact  he  discovered  these  metals 
by  electrolysis. 
In  all  these  experiments  it  is  found  that 


FIG.  7. 

the  weight  of  the  substances  liberated  by 
electrolysis  is  exactly  proportional  to  the 
quantity  of  electricity  that  has  passed  through 
the  cell.  It  is  also  found  that  if  the  same 
current  passes  through  different  cells  con- 
taining different  electrolytes,  the  weight  of  the 
different  substances  liberated  are  in  the  same 
proportion  as  their  chemical  equivalents.  These 
two  laws,  both  discovered  by  Faraday,  are 
known  as  Faraday's  first  and  second  law  of 
electrolysis.  The  electrochemical  equivalent 


THE  ELECTRIC   CURRENT       125 

of  a  substance  is  the  weight  in  grams  liberated 
by  the  passage  of  one  unit  of  electricity.  The 
unit  here  chosen  is,  however,  not  the  small 
electrostatic  unit  as  defined  on  p.  13,  but 
the  arbitrary  unit  called  the  Coulomb,  after 
the  French  physicist,  and  is  represented  by 
that  quantity  of  electricity  which  would 
accumulate  on  a  conductor  if  it  were  charged 
with  a  current  of  one  ampere  for  one  second. 
We  may  even  take  a  larger  unit,  such  as  the 
ampere-hour,  as  the  unit  to  which  the  quantity 
of  electrolytically  deposited  substances  may 
be  referred.  The  ampere-hour  is  equal  to 
3,600  coulombs.  The  following  table  gives, 
for  a  few  substances,  the  weight  deposited 
by  one  ampere-hour  of  electricity — 


Hydrogen 

Oxygen 

Water 

Copper 

Zinc 

Silver 


Grams  per 
ampere-hour. 

0-037 
0-298 
0-335 
1-182 
1-215 
4-032 


By  means  of  such  figures  it  is  possible  to 
determine  beforehand  the  quantity  of  electri- 
city which  must  be  passed  through  a  cell  in 
order  to  deposit  a  certain  weight  of  metal 


126  ELECTRICITY 

on  the  objects  to  be  treated.  Conversely,  it 
is  also  possible  to  draw  up  a  balance  sheet 
showing  how  much  zinc  will  be  used  up  in  a 
voltaic  cell  relatively  to  the  amount  of  electri- 
city obtained  from  the  cell.  Such  a  balance 
sheet  shows  that  the  production  of  electric 
currents  in  large  quantities  by  voltaic  cells  is 
far  too  expensive  for  commercial  use.  It  is 
only  when  feeble  currents  are  required  that  it 
pays  to  produce  current  'by  electrolytic  pro- 
cess ;  when  current  is  required  on  a  large  scale, 
such  as  for  lighting  and  power,  and  also  for 
metallurgical  work,  copper  refining  and  electro- 
plating on  a  large  scale,  it  must  be  produced 
by  dynamo  machines.  Electrolysis,  then,  is 
not  of  much  importance  for  the  production 
of  electricity,  but  it  is  of  enormous  importance 
in  the  utilisation  of  electricity,  forming  the 
basis  of  copper  refining  and  electro -plating,  on 
which  large  industries  carried  on  in  Swansea, 
Birmingham,  Sheffield  and  other  places  are 
built  up. 

Thermal  action  of  an  electric  current. — An 
electric  current  flowing  through  any  conductor 
heats  it.  The  amount  of  heat  developed 
depends  on  the  material  of  the  conductor, 
its  length,  cross  section  and  the  strength  of 
the  current.  As  the  current  is  increased 


THE  ELECTRIC  CURRENT       127 

the  heat  increases  also,  but  at  a  faster  rate, 
so  that  if  the  conductor  is  a  wire  a  point  is 
reached  when  it  becomes  red-,  or  white-hot, 
and  gives  out  light.  This  is,  indeed,  the 
principle  on  which  incandescent  lamps  be- 
come sources  of  light.  The  wire  may  be  a 
carbon  filament,  or  a  filament  of  tantalum, 
tungsten,  or  other  highly  refractory  metal. 
Whatever  the  substance  used  for  the  filament 
of  a  lamp,  it  is  subject  to  the  same  influence 
as  any  other  conductor — it  gets  hot  when 
traversed  by  a  current.  There  is,  however, 
this  difference  in  degree.  In  the  lamp  we 
desire  to  produce  heat  at  a  high  temperature, 
for  only  then  do  we  get  light  as  well  as  heat ; 
in  a  conductor  used  for  the  purpose  of  trans- 
ferring electricity  from  the  source  where  it  is 
generated  to  the  apparatus  where  it  is  utilised, 
we  desire  to  generate  as  little  heat  as  possible. 
There  is  an  advantage  in  producing  a  high 
temperature  in  the  filament  of  the  incandescent 
lamp,  but  there  is  no  advantage  whatever  in 
producing  heat  in  the  wires  that  carry  the 
current  to  the  lamp.  On  the  contrary,  there 
is  an  objection  to  it;  not  only  does  the 
generation  of  heat  mean  a  dissipation  of 
energy,  that  is,  of  something  which  costs 
money,  but  it  may  be  a  positive  danger,  since 


128  ELECTRICITY 

a  conductor  becoming  red-hot  may  set  fire  to 
a  building. 

To  guard  against  this  danger  a  short  piece 
of  the  conductor  is  made  very  thin,  so  that  in 
the  event  of  the  current  becoming  so  strong 
that  the  rest  of  the  conductor  becomes  sensibly 
hot,  this  little  piece  shall  become  so  hot  that 
it  fuses,  and  thus  interrupts  the  continuity  of 
the  conductor,  that  is,  causes  an  interruption 
of  the  current.  This  is  the  principle  of  pro- 
tecting electric  circuits  against  overheating. 
The  short  bit  of  the  conductor,  intended  by  its 
destruction  to  save  the  rest,  is  called  the  fuse, 
and  this  is  so  placed  that  by  its  melting  it 
cannot  cause  a  fire.  Such  fuses  are  found  in 
every  domestic  installation  for  lighting.  The 
fuse  wire  is  enclosed  in  a  tube  or  plug  of 
porcelain,  and  sometimes  the  cavity  is  filled 
in  with  carborundum  powder  to  act  as  an 
absorbent  of  the  heat  momentarily  generated 
by  the  explosive  fusion  of  the  wire. 

In  this  connection  it  is  interesting  to  note  that 
the  seemingly  obvious  is  not  always  the  best. 
At  first  fuse  wires  were  made  of  tin  or  lead, 
simply  because  these  metals  fuse  at  a  low  tem- 
perature, and  it  seemed  obvious  that  the  lower 
the  temperature  of  fusion  the  quicker  would 
the  device  act.  This  is  a  fallacy.  If  lead  or 


THE  ELECTRIC   CURRENT       129 

tin  are  used  for  the  fuse  wire,  this  must  be  much 
stouter  than  would  be  the  case  with  copper  or 
silver ;  consequently  the  amount  of  material, 
which  by  the  heating  is  volatilised,  becomes  so 
great  that  the  process  resembles  rather  an 
explosion  than  a  quiet  melting,  and  the  enve- 
lope may  be  shattered,  letting  out  the  flash, 
and  thus  the  fuse  itself  may  become  a  source 
of  danger.  In  this  respect  the  best  material 
for  fuse  wires  is  silver.  An  exceedingly  .thin 
silver  wire  will  carry  a  fairly  large  current,  and 
if  the  current  should  rise  to  a  dangerous  value 
and  the  wire  be  fused,  the  amount  of  material 
volatilised  is  so  small  that  there  is  hardly  any 
explosive  effect,  especially  if  the  wire  is  em- 
bedded in  carborundum  powder. 

Now  the  reader  may  ask,  why  should  a  thin 
silver  wire  suffice  if  for  the  same  current  a 
stout  lead  wire  is  necessary  ?  This  comes 
from  the  physical  fact  that  silver  is  far  better 
adapted  than  lead  for  carrying  an  electric 
current,  it  conducts  better,  or,  as  we  also  may 
say,  it  has  a  higher  "  conductivity."  By  this 
we  mean  that  to  get  the  current  through  the 
wire  the  force  which  is  pushing  the  electricity 
from  one  end  to  the  other  is  much  smaller  with 
silver  than  with  lead ;  silver  offers  less  "  re- 
sistance "  to  the  flow  of  electricity  than  lead. 
i 


130  ELECTRICITY 

Thus  each  conductor  has  a  certain  physical 
property  called  its  electric  resistance,  and  this 
depends  on  the  length  and  section  of  the 
conductor,  on  its  temperature  and  on  its 
material.  In  order  to  compare  different 
materials  as  regards  resistance,  we  must 
eliminate  those  elements  which  may  vary 
from  case  to  case  and  reduce  all  to  the  same 
standard.  The  physicist  takes  as  the  standard 
length  the  centimetre,  and  as  the  standard 
cross  section  the  square  centimetre.  The 
standard  form  for  which  the  resistance  is  given 
is  thus  not  a  wire  at  all,  but  a  cube.  The 
engineer  prefers  to  retain  the  shape  of  the  wire 
for  his  standard,  and  defines  the  resistance  of 
the  material  as  that  of  a  wire  one  metre  long 
and  one  square  millimetre  in  cross  section,  the 
test  being  made  at  the  temperature  of  15°  C. 
How  is  such  a  test  to  be  made  ?  G.  S. 
Ohm,  a  Bavarian  physicist  (1787-1854),  was 
the  first  to  make  such  tests  and  to  formu- 
late a  law,  which  bears  his  name,  and  which 
connects  the  three  things  on  which  the 
transfer  of  electricity  from  one  end  of  a  con- 
ductor to  the  other  depends.  Ohm  found 
experimentally  that  the  strength  of  the 
current  is  directly  proportional  to  the  e.m.f. 
applied  at  the  ends  of  the  wire,  and  inversely 


THE  ELECTRIC  CURRENT       131 

proportional  to  a  particular  physical  property 
which,  he  called  the  "  resistance  "  of  the  wire. 
Expressed  mathematically,  Ohm's  law  is 


where  I  stands  for  current  strength,  E  for 
electromotive  force,  and  R  for  resistance. 
He  also  found  that  in  a  double  length  of  wire 
the  same  e.m.f.  will  only  produce  half  the 
current  strength,  whilst  by  increasing  the  cross 
section  of  the  wire  (which  can  conveniently 
be  done  by  using  two  or  more  wires  side  by 
side),  the  current  strength  is  proportionately 
increased.  He  thus  found  that  the  resistance 
of  the  conductor  is  directly  proportional  to 
its  length  and  inversely  proportional  to  its 
section.  This,  again  expressed  mathematically, 
is 


where  L  is  the  length  and  q  the  section.  The 
coefficient  Q  depends  on  the  material,  and  is 
called  "  the  specific  resistance."  The  two 
formulae  here  given  are  generally  valid,  what- 
ever may  be  the  system  of  units  chosen. 
They  may,  therefore,  also  be  used  with  the 
practical  units  of  the  "  ampere  "  for  current 


132 


ELECTRICITY 


strength  and  the  "  volt  "  for  e.m.f.,  in  which 
case  the  unit  of  resistance  is  called  the  "  ohm." 
The  following  table  gives  the  specific  resistance 
reduced  to  a  standard  wire  one  metre  in  length 
and  one  square  millimetre  in  cross  section  at 
ordinary  room  temperature — 


Material. 

Silver 

Copper 

Aluminium 

Iron 

Mercury    . 

Platinum 


Resistance  in  ohms. 
0-0158 
0-0165 
0-0287 
0-125 
0-953 
0-094 


The  fact  that  a  column  of  mercury  one  metre 
long  and  one  square  millimetre  in  section  has  a 
resistance  of  nearly  an  ohm,  has  led  to  sug- 
gestions to  adopt  mercury  as  a  standard  of 
resistance,  and  indeed,  before  the  true  value 
of  the  ohm  had  been  determined  by  electro- 
dynamic  investigation,  the  mercury  column 
was  taken  as  approximately  representing  an 
ohm.  It  might  be  thought  that  such  a 
standard  would  be  acceptable  to  physicists, 
because  it  would  enable  each  investigator  to 
reproduce  the  standard  at  any  time  for  him- 
self, and  thus  render  him  independent  of 
others.  It  is,  however,  not  at  all  easy  to  pro- 
duce such  a  standard.  There  is  not  only  the 


THE   ELECTRIC   CURRENT       133 

difficulty  of  obtaining  a  glass  tube  of  absolutely 
even  bore,  but  the  further  difficulty  that  the 
specific  resistance  of  mercury,  as  of  all  metals, 
varies  slightly  with  the  degree  of  chemical 
purity  in  which  the  metal  can  be  obtained, 
so  that  the  so-called  "  mercury  standard  "  has 
been  discarded  in  favour  of  standards  made  of 
platinum. 

Such  standards  are  deposited  in  State 
Laboratories  or  Museums,  and  only  serve 
as  reference  standards,  such  as  the  yard  or 
the  pound.  For  practical  use  other  so-called 
secondary  standards  are  made  of  some  less 
expensive  material,  generally  some  alloy,  such 
as  German  silver,  manganin,  platinoid,  eureka 
metal,  etc.  These  alloys  have  the  advantage 
that  their  resistance  is  very  little  influenced 
by  change  in  temperature,  whereas  copper 
increases  its  resistance  sensibly  when  heated. 
For  every  degree  centigrade  of  temperature 
rise  above  15°  C.,  the  resistance  of  a  copper 
conductor  rises  by  about  0-38  per  cent.  All 
machines  when  at  work  become  heated  to  a 
certain  extent,  since  some  of  the  energy  which 
is  passing  through  the  machine  is  necessarily 
lost  in  the  process  of  conversion  from  one  form 
to  another  form.  This  lost  energy  is  con- 
verted into  heat,  and  thus  the  temperature  of 


134  ELECTRICITY 

the  machine  is  increased.  The  more  efficient 
the  machine,  that  is  to  say,  the  less  of  the 
energy  passing  through  it  is  lost,  the  cooler 
will  the  machine  run.  Excessive  heating  in 
a  machine  is  also  objectionable  on  the  ground 
that  thereby  some  of  the  materials  used  in  the 
construction  may  be  destroyed. 

If  we  have  to  deal  with  a  dynamo  machine 
this  is  especially  important,  since  in  the 
construction  of  such  machine  insulating 
materials  such  as  cotton,  tape,  wood,  etc., 
must  be  used.  The  machine  should  therefore 
be  designed  with  due  regard  to  a  strictly 
limited  temperature  rise,  and  it  is  also  im- 
portant that  the  finished  machine  should  be 
tested  so  as  to  make  sure  that  the  designer's 
intention  has  actually  been  realised.  The  heat 
is  generated  in  the  body  of  the  materials 
used,  and  it  has  to  leak  out  and  be  dissipated 
into  the  surrounding  atmosphere  from  the 
surface  of  the  machine.  Thus  it  is  quite 
possible  that  the  temperature  at  the  surface, 
which  can  be  measured  by  a  thermometer,  is 
much  below  the  internal  temperature,  just 
as  the  outer  surface  of  a  stove  is  not  nearly  so 
hot  as  the  fire  inside.  To  get  the  temperature 
of  the  hottest  part,  we  should  put  a  ther- 
mometer to  the  inside  of  the  machine,  but 


THE  ELECTRIC   CURRENT       135 

unless  provision  has  been  made  in  the  con- 
struction of  the  machine  for  such  application 
of  thermometers,  this  may  not  be  done.  It  is 
in  this  connection  that  the  influence  of 
temperature  on  the  resistance  of  copper 
comes  in  very  useful.  We  need  only  measure 
the  resistance  of  the  copper  coils  before  the 
machine  is  set  to  work,  that  is  to  say,  whilst 
it  is  at  ordinary  room  temperature,  and  repeat 
the  measurement  after  the  machine  has  got 
hot  through  working.  The  increase  of  re- 
sistance thus  found  may  be  used  to  calculate 
the  rise  of  temperature  in  the  interior  of  the 
machine.  According  to  the  best  modern 
practice,  this  rise  should  not  exceed  about 
50°  C. 

Another  important  application  of  the  fact 
that  all  metals  increase  their  resistance  with 
a  rising  temperature  is  made  in  the  so-called 
"  electric  pyrometer,"  an  instrument  for 
measuring  the  very  high  temperatures  in 
metallurgical  furnaces.  Essentially,  the  pyro- 
meter consists  of  a  porcelain  tube  containing 
a  spiral  of  platinum  wire,  which  is  put  into 
the  furnace.  The  spiral  is  joined  to  other 
wires  of  low  resistance,  which  lead  to  some 
kind  of  measuring  instrument,  indicating  the 
resistance  of  the  platinum  spiral.  The  hotter 


136  ELECTRICITY 

the  furnace,  the  higher  becomes  the  resist- 
ance of  the  spiral,  so  that  by  a  suitable 
graduation  of  the  scale  of  the  instrument, 
this  may  be  used  to  show  what  temperature 
actually  exists  in  the  furnace. 

The  influence  of  temperature  on  the  re- 
sistance of  a  material  is  a  physical  attribute 
of  the  material,  such  as  its  specific  resistance 
itself,  or,  for  the  matter  of  that,  as  all  its 
physical  and  chemical  properties.  We  express 
this  particular  property  by  saying  that  the 
material  has  such  and  such  a  "  temperature 
coefficient."  Thus  copper  has  a  temperature 
coefficient  of  +  0-0038,  meaning  that  the 
resistance  increases  by  0-38  per  cent,  for  every 
degree  of  temperature  increase.  The  -f-  sign 
means  that  the  coefficient  is  positive,  that  is, 
refers  to  an  increase,  not  a  decrease  of  re- 
sistance. There  are,  however,  certain  sub- 
stances which  have  a  negative  temperature 
coefficient.  In  these  materials  the  resistance 
diminishes  as  they  get  hotter.  Most  liquid 
conductors  have  this  property,  and  of  solid 
conductors  carbon  is  a  familiar  example. 
The  resistance  of  a  carbon  filament  incan- 
descent lamp  is  greater  when  the  lamp  is  cold 
than  when  it  is  alight.  In  this  case  the  heat 
is  generated  by  the  current  passing  through 


THE  ELECTRIC  CURRENT       137 

the  filament.  If  then,  by  raising  the  e.m.f. 
of  the  supply  more  current  passes  through 
the  lamp,  the  filament  gets  hotter,  its  re- 
sistance decreases,  and  still  more  current  is 
permitted  to  pass.  The  result  of  this  inter- 
action is  that  an  increase  of  voltage  does  not 
produce  a  proportional,  but  an  exaggerated 
increase  of  current  and  vice 'versa,  with  a 
corresponding  exaggerated  variation  in  the 
light  given.  Such  lamps  are  sensitive  to 
changes  in  voltage,  more  so  than  the  metal 
filament  lamps  which,  by  reason  of  their 
positive  temperature  coefficient,  burn  with 
greater  stability. 

The  most  sensitive  of  all  filaments  is,  how- 
ever, the  pencil  of  a  "  Nernst "  lamp.  This, 
when  cold,  is  not  a  conductor  at  all;  to 
make  it  conducting  it  must  be  heated  to 
a  dull  red  heat  by  a  platinum  spiral  placed 
near  it  in  the  lamp.  When  sufficiently  hot 
the  pencil  becomes  a  conductor  of  considerable 
resistance,  so  that  a  much  shorter  length  than 
the  filament  of  a  metal  or  carbon  lamp  offers 
sufficient  resistance  for  a  working  e.m.f.  of  200 
or  220  volts.  By  the  passage  of  the  current  the 
pencil  is  maintained  at  white  heat,  and  a  very 
brilliant  light  is  emitted.  The  pencil  is,  how- 
ever, very  sensitive  to  changes  in  voltage.  It 


138  ELECTRICITY 

has  a  very  large  negative  temperature  coeffi- 
cient, and  in  consequence  the  exaggeration  as 
regards  changes  in  current  strength  mentioned 
on  the  previous  page  in  connection  with  carbon 
lamps,  is  much  greater ;  in  fact,  it  is  so  great 
that  the  working  becomes  unstable  if  the 
pencil  be  used  alone,  even  on  a  circuit  of 
perfectly  constant  voltage.  To  make  the 
use  of  such  a  pencil  possible,  it  is  necessary 
to  protect  it  against  excess  of  current  and 
consequent  disintegration.  This  is  done  by 
correcting  its  negative  temperature  coefficient 
by  the  addition  of  a  conductor  having  a  large 
positive  temperature  coefficient.  Such  a  con- 
ductor is  iron  when  near  the  point  of  red  heat. 
The  pencil  and  this  additional  resistance, 
termed  technically  a  "  ballast  resistance " 
are  arranged  tandem-fashion,  or,  as  it  is  called, 
"  in  series,"  so  that  the  current  first  passes 
through  the  ballast  resistance  and  then 
through  the  pencil.  The  object  of  the  ballast 
resistance  is  to  keep  the  current  as  near 
constant  as  possible ;  and  this  object  is  attained 
by  the  fact  that,  owing  to  the  peculiar  property 
of  hot  iron  to  very  largely  increase  its  re- 
sistance for  even  a  slight  increase  of  tempera- 
ture, the  e.m.f.  absorbed  by  the  ballast 
resistance  becomes  large  even  with  a  small 


THE  ELECTRIC  CURRENT       139 

increase  of  current,  so  that  a  further  growth 
of  current  is  efficiently  checked.  It  is  in 
this  way  that  the  working  of  the  Nernst 
lamp  is  made  stable. 

The  ballast  resistance  is  made  of  fine  iron 
wire ;  and  if  this  were  allowed  to  become  nearly 
red-hot  whilst  exposed  to  the  air,  it  would  very 
soon  burn  out.  It  is  therefore  necessary  to 
protect  this  delicate  spiral  of  wire  from  the  air, 
and  this  is  done  by  enclosing  it  in  a  sealed  glass 
tube.  This  tube  is  filled  with  hydrogen,  since 
hydrogen  has,  of  all  gases  which  could  be 
used  in  this  case,  the  greatest  heat  capacity. 
It  would  obviously  be  a  mistake  to  use  an 
exhausted  tube  as  a  protecting  envelope  for 
the  iron  spiral,  since  through  a  vacuum  very 
little  heat  can  be  transmitted,  and  it  is  obvi- 
ously important  to  prevent  the  spiral  from 
getting  more  than  dull  red-hot,  otherwise  it 
would  be  destroyed.  If,  then,  a  gaseous 
filling  is  indispensable  for  the  conveyance  of 
the  heat  generated  in  the  spiral  to  the  out- 
side envelope,  we  must  use  a  gas  which  will 
not  burn  the  iron.  Air  is  therefore  inad- 
missible. Nitrogen  or  carbonic  acid  might 
be  used,  but  these  gases  do  not  convey  heat 
so  readily  as  hydrogen,  the  lightest  of  all 
gases,  and  whose  molecules  are  the  most 


140  ELECTRICITY 

mobile.  Similar  resistances  are  also  used  as 
regulating  devices  in  train  lighting.  Regulat- 
ing resistances  of  this  kind,  but  on  a  much 
larger  scale,  are  now  made  for  various  in- 
dustrial purposes  where  it  is  important  to 
keep  a  current  fairly  constant,  notwithstand- 
ing variations  in  resistance  or  e.m.f. 


CHAPTER  VI 

THE   DYNAMICS    OF   ELECTRIC   CURRENTS 

WE  have  seen  that  two  carriers  of  static 
charges,  if  brought  near  each  other,  act  upon 
each  other  with  a  certain  mechanical  force. 
The  same  is  the  case  with  conductors  carrying 
moving  charges,  that  is  to  say,  electric  currents 
under  certain  conditions.  The  two  con- 
ductors must  lie  near  each  other  and  run  more 
or  less  parallel.  If  the  two  currents  flow  in 
the  same  direction  the  wires  attract  each 
other,  if  they  flow  in  opposite  directions  the 
wires  repel  each  other.  The  fact  that  parallel 
currents  flowing  in  the  same  direction  attract 
each  other  may  be  proved  by  a  very  simple 
experiment :  Take  a  loosely  coiled  hank  of 
fine,  and  therefore  very  flexible,  cotton-covered 
copper  wire,  hang  it  over  a  bar,  and  send  a 
current  through  it.  Immediately  on  closing 
the  switch,  which  completes  the  circuit  through 
the  hank  of  wire  and  allows  the  current  to 
flow,  we  shall  observe  a  tightening  up  of  the 
141 


142  ELECTRICITY 

loose  hank  into  a  more  compact  mass  of  coils. 
On  opening  the  switch,  the  elasticity  of  the 
single  turns  causes  them  to  spread  out  again 
from  each  other.  In  such  a  coil  all  wires 
carry  the  same  current,  they  are  more  or  less 
parallel,  and  the  direction  of  flow  is  the  same. 
The  force  which  this  simple  experiment 
reveals  is  but  feeble,  but  in  kind  it  is  the  same 
force  which  comes  into  play  when  we  use 
electricity  for  driving  a  1000  horse- power 
rolling-mill,  or  a  tram-car  or  a  railway  train. 
The  difference  is  merely  one  of  degree  as 
regards  the  magnitude  of  the  force,  and  of 
suitable  arrangement  of  the  parts  of  the 
machine,  so  that  instead  of  one  spasmodic  jerk 
of  the  outermost  loose  coils  of  our  hank  we 
shall  get  a  sustained  rotary  movement  of  all 
the  coils. 

The  increase  in  the  magnitude  of  the  force 
is  brought  about  by  the  use  of  iron.  That  the 
increase  is  very  considerable  may  be  shown 
by  a  simple  experiment :  Take  two  paper 
tubes  about  an  inch  in  diameter  and  four 
inches  long.  Wind  on  each  about  ten  layers 
of  fine  cotton-covered  copper  wire,  so  as  to  get 
a  long  coil  containing  about  500  or  1000  turns 
in  all.  Leave  the  two  ends  of  the  wire  long 
enough  to  serve  as  suspending  wires  of  the 


DYNAMICS  143 

coil.  A  coil  of  this  kind  is  called  a  "  solenoid." 
If  two  such  solenoids  are  suspended  horizon- 
tally from  their  own  wires  one  behind  the 
other,  so  that  the  axes  are  in  the  same  line, 
with  their  ends  half -an- inch  apart,  it  will  be 
found  that  on  sending  a  current  through 
them  they  will  either  repel  or  attract  each 
other.  If  the  direction  of  the  current  round 
the  spiral  of  both  coils  is  the  same,  there  will 
be  attraction ;  if  the  current  direction  in  one 
solenoid  is  reversed,  there  will  be  repulsion. 
In  both  cases  the  force  is  feeble. 

Now  place  into  the  paper  tube  of  each 
solenoid  an  iron  core.  The  force  will  now  be 
very  much  increased.  If  the  coils,  instead  of 
being  suspended,  be  held  fast,  and  the  cores 
can  slide  easily  within  their  paper  tubes,  it  will 
be  found  that  the  cores  themselves  either  come 
together  or  fly  apart  according  to  the  relative 
direction  of  the  current.  Thus  the  presence 
of  the  iron  not  only  increases  the  dynamic 
force  of  the  current,  but  it  also  shifts  the  seat 
of  this  force  from  the  wire  to  the  iron.  We  are 
thus  driven  to  the  conclusion  that  the  seat  of 
the  force,  or  at  least  part  of  it,  is  not  in  the  wire 
itself,  but  in  the  space  surrounding  the  wire. 

The  fact  that  an  electric  current  pro- 
duces mechanical  forces  acting  through  space 


144  ELECTRICITY 

was  first  discovered  by  the  Danish  Physicist 
Oersted  (1777-1851),  not  by  the  experiment 
here  described,  but  in  a  still  more  simple  way. 
He  found  that  if  a  wire  carrying  a  current 
is  placed  above  and  parallel  to  the  needle  of  a 
compass,  the  needle  is  deflected.  The  deflec- 
tion is  in  one  sense  with  the  current  flowing 
one  way,  and  in  the  opposite  sense  if  the 
current  is  reversed.  The  deflection  is  in- 
creased if  the  strength  of  the  current  is 
augmented,  or  the  wire  brought  nearer. 
There  is  no  deflection  if  the  wire  is  placed 
not  over,  but  parallel  to  and  at  the  side  of  the 
needle;  and  if  the  wire  is  shifted  from  a 
position  parallel  to  and  above  the  needle  to 
a  similar  position  and  distance  below  the 
needle,  the  deflection  is  reversed.  Also,  if  the 
wire  is  not  exactly  parallel  to  the  direction 
in  which  the  needle  points,  there  is  some 
deflecting  force,  though  this  gets  weaker  as 
the  angle  between  wire  and  needle  increases. 
All  these  facts  the  reader  may,  by  the  aid  of 
a  pocket  compass,  a  voltaic  cell  and  a  few 
feet  of  wire,  find  out  for  himself. 

To  us  in  1912  there  is  nothing  remarkable 
about  such  an  experiment ;  but  when  Oersted 
first  performed  it  in  1820  it  was  a  revelation 
of  enormous  import.  The  scientific  world  of 


DYNAMICS  145 

those  days  knew  something  of  electricity,  and 
it  knew  something  of  magnetism,  but  it  knew 
these  two  things  as  distinct  from  each  other. 
Now  by  one  stroke  of  experimental  genius 
Oersted  showed  the  scientific  world  that,  after 
all,  electricity  and  magnetism  are  not  inde- 
pendent domains  of  physics,  but  are  intimately 
connected.  Every  physicist  in  Europe  re- 
peated the  experiment,  and  many  speculated 
on  the  question  what  really  constituted  the 
connecting  link  between  magnetic  and  electric 
phenomena.  It  was  Ampere  who  first  formu- 
lated a  rule  by  which  the  direction  of  deflection 
could  be  predicted,  and  two  other  French 
scientists,  Messrs.  Biot  and  Savart,  gave  a 
mathematical  formula  by  which  the  magni- 
tude of  the  deflecting  force  could  be  calculated. 
Ampere's  rule  is  as  follows  :  Imagine  yourself 
swimming  in  the  direction  of  the  electric 
current  and  looking  at  the  compass  needle. 
Its  north  end  will  then  be  deflected  to  your 
left.  Biot-Savart's  law  may  be  stated  by 
reference  to  the  force  exerted  by  the  current 
on  unit  magnetic  matter  at  any  given  point 
of  the  space  in  the  neighbourhood  of  the 
conductor. 

Before  discussing  this  subject  it  is  necessary 
to  define  what  we  mean  by  the  term  "  unit 
K 


146  ELECTRICITY 

of  magnetic  matter."  It  has  already  been 
mentioned  that  it  is  physically  impossible 
to  isolate  north  from  south  magnetism  as 
completely  as  we  can  isolate  positive  from 
negative  electric  charges.  Magnetism  always 
appears  as  an  attribute  of  a  magnetic 
material,  such  as  steel  ;  and  when  one  end  of 
a  steel  bar  shows  north  magnetisation,  the 
other  shows  south  magnetisation.  Thus  a 
perfect  isolation  of  magnetic  matter  of  one 
kind  is  not  possible.  The  isolation  can  only 
be  partial,  but  this  need  not  deter  us  from 
assuming,  merely  for  the  purpose  of  a  defini- 
tion, that  at  a  particular  point,  say  the  end  of 
a  long  wire,  a  definite  amount  of  north 
magnetic  matter  is  accumulated,  whilst  the 
corresponding  south  end  of  the  wire  is  so  far 
removed  that  it  does  not  interfere  with  any 
test  we  may  make.  Imagine,  then,  that  we 
have  in  two  points  of  space,  D  cm.  apart,  the 
magnetic  masses  M  and  m  concentrated.  The 
force  acting  between  them  is,  by  the  general 
law  discussed  in  Chapter  I,  given  by  the 
expression 


D2 

Let  M  be  fixed  in  space  and  move  m  round 
it  on  the  surface  of  a  sphere,  then  the  same 


DYNAMICS  147 

force  will  be  experienced  at  any  point  of  the 
sphere,  and  the  only  thing  that  changes  will 
be  the  direction  of  the  line  along  which  the 
force  acts.  We  may  in  fact,  analogous  with 
the  argument  used  in  the  consideration  of  the 
electrical  problem,  consider  the  magnetic 
force  as  an  attribute  of  space  and  express  it 
by  the  product  B  x  m,  where  B  indicates  the 
density  of  the  magnetic  field  on  the  surface 
of  the  sphere  of  radius  D.  B  is  the  "  induc- 
tion "  expressed  as  so  many  lines  of  force  per 
square  centimetre  of  surface,  and  the  product 
of  the  total  surface  of  the  sphere,  with  this 
induction,  will  give  the  total  flux  of  force  0 
emanating  from  the  magnetic  mass  M.  Since 

the  surface  of  a  sphere  is  4:rcD2  and  B  =  =^, 

we  find  the  following  relation  between  the 
quantity  of  magnetic  matter  M  and  the  total 
flux  0  emanating  from  it — 

0  =  4ftM 

We  are  now  in  a  position  to  define  unit  of 
induction  and  unit  of  magnetic  matter.  If 
two  magnetic  masses  placed  one  centimetre 
apart  attract  or  repel  each  other  with  the 
force  of  one  dyne,  then  each  magnetic  mass 
has  unit  value.  If  at  any  point  of  space  unit 


148  ELECTRICITY 

magnetic  mass  is  acted  upon  with  the  force 
of  one  dyne,  then  the  induction  at  that  point 
is  unity,  or,  as  we  also  may  express  it,  each 
square  centimetre  of  a  surface  laid  at  right 
angles  to  the  direction  of  the  force  at  that 
point  is  traversed  by  one  line  of  force.  Thus 
we  may  define  the  horizontal  component  of 
the  earth's  magnetism  by  saying  that  the 
induction  is  0-18,  meaning  thereby  that  each 
unit  of  magnetism  accumulated  on  the  north 
end  of  a  compass  needle  is  drawn  northwards 
with  a  force  of  0-18  dynes,  the  other  end  of 
the  needle  being  drawn  southward  with  an 
equal  force.  These  forces  make  the  needle 
point  north-south.  In  a  dynamo  machine 
there  is  also  magnetic  induction,  but  of  vastly 
greater  intensity.  In  such  machines  e.m.f.  is 
produced  by  the  motion  of  wires  placed  on  an 
armature,  which  revolves  within  a  system  of 
magnet  poles.  The  clearance  space  between 
the  face  of  the  poles  and  the  surface  of  the 
armature  is  traversed  by  magnetic  lines  of 
force,  and  the  stronger  the  induction  in  this 
so-called  "  air  space,"  the  higher  is  the  e.m.f. 
of  the  machine.  The  object  of  the  designer 
is  therefore  to  produce  as  strong  an  induction 
as  possible.  In  modern  machines  the  induc- 
tion in  the  air  space  is  of  the  order  of  5000  to 


DYNAMICS  149 

10,000,  and  each  square  centimetre  of  polar 
surface  contains  something  like  400  to  800 
units  of  magnetic  matter. 

We  now  return  to  the  consideration  of  Biot- 
Savart's  law.  The  definition  given  by  them 
is  as  follows :  The  force  exerted  on  unit 
magnetic  mass  at  a  given  point  (or,  as  we 
may  also  say,  the  induction  at  that  point), 
due  to  an  element  of  the  conductor,  is  given 
by  the  expression  :  product  of  the  length  of 
the  element  as  seen  from  that  point,  the 
strength  of  the  current;  and  this  divided 
by  the  square  of  the  distance.  Stated  in 
this  form  the  law  sounds  rather  complicated, 
but  it  becomes  simple  enough  if  we  apply  it 
to  some  special  cases.  Take,  for  instance,  a 
circular  conductor.  The  induction  in  its 
centre,  produced  by  an  element  of  one  centi- 
metre length  of  the  conductor,  would  be 
simply  the  product  of  the  current  multiplied 
with  the  visible  length  (in  this  case  also  a 
centimetre),  and  this,  divided  by  the  square 
of  the  radius  R.  Since  in  the  whole  circle 
there  are  2nR  such  elements,  the  induction, 
due  to  the  whole  of  the  conductor  carrying  a 
current  J,  is 


150  ELECTRICITY 

The  force  acts  at  right  angles  to  the  plane  of 
the  circular  loop.  A  unit  pole  will  therefore 
be  drawn  through  the  loop  with  the  force 


By  means  of  this  formula  we  may  now 
define  unit  current.  If  J  =  1  and  R  =  1,  then 
B  =  2n.  Now  imagine  a  wire  bent  into  a 
circle  of  1  cm.  radius.  If  unit  pole  in  the  centre 
of  this  circle  is  drawn  through  it  with  a  force 
of  6*28  dynes,  then  there  is  unit  current  in 
the  wire.  This  so-called  electromagnetic  unit 
of  current  strength  is  too  large  for  practical 
work,  and  for  this  reason  a  unit  ten  times 
smaller  is  adopted.  This  is  called  the  ampere. 

The  coil  exerts   a    force  F  =  —  ^—  dynes 

on  the  magnetic  mass  m  placed  in  the  centre 
of  its  plane,  but  since  action  and  reaction 
must  always  be  equal,  this  is  also  the  force 
with  which  the  mass  m  acts  on  the  wire. 
The  induction  due  to  m  in  the  space  occupied 

by  the  wire  is  B  =  ^2  ,  and  by   combining 

the  equations  for  F  and  B  we  find  F  =  2^RJB 
dynes. 
This  is  the  force  experienced  by  a  wire  of 


DYNAMICS  151 

2nR  cm.  length,  carrying  a  current  of  J  units 
in  a  field  of  induction  B.  Generally,  writing 
I  for  the  length  of  the  wire  in  cm.,  and  express- 
ing current  strength  in  amperes,  we  have  the 
force  in  dynes 


Let  us  apply  this  to  the  wire  on  the  armature 
of  a  dynamo  machine.  Suppose  the  armature 
is  10",  or  25*4  cm.  long,  and  the  induction  is 
8000.  With  a  current  of  50  amperes  through 
the  wire  we  have  a  tangential  force  of 

Kf\ 

F  =  ^25-4,  8000  dynes; 

or, 
F  =  1-03  Kg.,  orF  =  2ilb. 

Since  on  the  circumference  of  an  armature 
there  may  be  hundreds  of  such  wires,  the 
majority  of  them  simultaneously  under  the 
same  influence,  it  is  easy  to  understand  that 
the  combined  tangential  force,  which  in  the 
case  of  an  electric  generator  has  to  be  over- 
come by  the  force  of  the  driving  engine,  and 
in  the  case  of  an  electromotor  produces 
motion,  may  become  very  considerable. 

In    deducing    the    formula    for    the    force 


152  ELECTRICITY 

between  a  current  and  a  magnetic  field,  we 
started  from  the  simple  case  of  a  wire  bent  in 
the  form  of  a  circle.  Let  us  use  a  coil  of 
many  turns,  then  the  total  volume  of  current 
flowing  round  the  circle  will  be  the  product 
of  the  current  and  the  number  of  turns.  If 
we  count  the  current  in  amperes,  we  may 
express  the  total  volume  of  current  as  so 
many  "  ampere-turns."  With  i  amperes  and 
n  turns  the  induction  in  the  centre  of  the 
coil  will  now  be 

,-,      ni  27t 
=  T6R 

Let  us  now  suspend  a  small  magnet  in  the 
centre  of  the  coil;  it  ought  to  be  small,  so 
that  both  its  poles  may  be  considered  as 
being  simultaneously  in  the  centre  of  the  coil, 
since  for  this  spot  only  is  the  formula  for  F 
valid.  One  end  of  the  needle  will  be  deflected 
to  one  side,  and  the  other  to  the  opposite 
side  of  the  plane  of  the  coil ;  in  other  words, 
the  needle  will  try  to  set  itself  at  right  angles 
to  the  plane  of  the  coil,  and  if  there  were  no 
other  forces  acting  on  it,  it  would  actually 
take  up  this  position.  Let  the  plane  of  the 
coil  be  north- south  so  that  the  needle,  before 
a  current  is  sent  through  the  coil,  lies  in  its 


DYNAMICS  153 

plane.  On  sending  the  current  through  the 
coil,  a  magnetic  field  is  produced  in  the 
centre,  the  lines  of  force  of  which  run  east- 
west,  that  is  to  say,  at  right  angles  to  the 
lines  of  force  representing  the  horizontal  com- 
ponent of  terrestrial  magnetism.  The  needle 
is  now  under  the  influence  of  two  forces,  one 
due  to  the  earth  trying  to  keep  it  in  a  north- 
south  position,  and  the  other  due  to  the 
current  in  the  coil  trying  to  place  it  east-west. 
The  true  position  it  will  actually  adopt  will 
be  a  compromise  between  these  two  tendencies. 
If  the  influence  of  the  coil  is  equally  strong 
with  that  of  the  earth,  the  needle  will  point 
north-west-south-east;  it  will  have  a  de- 
flection of  45°.  If  the  current  is  made 
weaker,  the  deflection  will  diminish ;  if  made 
stronger,  it  will  increase.  In  this  way,  by 
observing  the  deflection  of  the  needle,  we 
can  determine  what  is  the  strength  of  the 
current  flowing  through  the  coil.  An  instru- 
ment of  this  kind  is  called  a  "  tangent  galvano- 
meter," the  term  "  tangent  "  arising  from  the 
fact  that  the  numerical  ratio  of  the  two 
forces  acting  at  right  angles  is  equal  to  the 
geometrical  tangent  of  the  angle  of  deflection. 
If  we  were  quite  certain  of  the  value  of  the 
horizontal  component  H  of  terrestrial  magnet- 


154  ELECTRICITY 

ism,  an  instrument  of  this  kind  could  be  used 
as  a  standard  by  which  to  calibrate,  that  is, 
mark  the  scale  of  commercial  amperemeters, 
but  in  our  electric  age  of  tramways  running 
in  all  directions,  dynamos  working  in  almost 
every  building,  and  with  steel  joists  used  in 
the  construction  of  buildings,  the  value  of 
H  in  any  given  place  is  an  uncertain  and 
changing  quantity.  The  tangent  galvano- 
meter can  therefore  not  be  considered  as  an 
absolute  standard  for  current  measurements, 
as  it  was  considered  by  scientists  two 
generations  ago;  but  it  may  still  be  used 
for  the  measurement  of  very  feeble  currents 
if  proper  precautions  be  used.  Since  we 
must  standardise  the  instrument  in  any  case, 
there  is  no  need  to  make  the  coil  enormously 
large  in  comparison  with  the  size  of  the 
needle;  we  can  make  both  coil  and  needle 
very  small,  and  use  a  great  number  of  fine 
wire  turns  in  the  coil.  By  these  means  it 
is  possible  to  produce  an  instrument  which 
is  capable  of  measuring  the  one-millionth  part 
of  an  ampere  or  even  less.  It  is  obvious  that 
with  so  delicate  an  instrument  no  material 
pointer  to  indicate  the  deflection  can  be  used. 
The  pointer  is  in  fact  weightless,  being  formed 
by  a  beam  of  light  reflected  from  a  little 


DYNAMICS 


155 


mirror  which  is  cemented  on  to  the  magnet 
needle.  Such  instruments  are,  therefore,  called 
"  mirror  galvanometers."  The  light  from  a 
lamp  is  focussed  on  to  the  mirror  and  is  from 


there  reflected  to  a  semi-transparent  scale. 
On  sending  a  current  through  the  coil  the 
spot  of  light  on  the  scale  is  deflected  and  the 
amount  of  its  displacement  is  proportional  to 
the  current.  By  sending  a  known  current 


156  ELECTRICITY 

through  the  coil  and  observing  the  resulting 
deflection,  the  instrument  can  be  calibrated. 

For  the  measurement  of  heavy  currents 
such  as  are  used  in  lighting  or  power  work 
the  dynamic  force  between  a  current  and  a 
magnetic  field  may  also  be  utilised,  but  in  a 
somewhat  different  way.  Fig.  8  is  a  diagram- 
matic representation  of  the  principles  on  which 
such  instruments  are  constructed.  Within 
the  polar  cavity  of  a  permanent  steel  magnet 
N  S  is  placed  an  armature  A,  and  into  the 
ring-shaped  space  between  the  two  is  inserted 
a  coil  C  formed  of  fine  wire  and  delicately 
pivoted  in  the  centre  of  the  armature.  To 
the  coil  is  attached  a  pointer  suitably  counter- 
weighted.  The  coil  is  under  the  control  of 
a  spiral  spring  S  which  keeps  it  normally  in 
the  position  shown  in  the  sketch,  the  pointer 
standing  at  zero.  The  current  to  be  measured 
I  is  flowing  along  the  wire  c  d,  and  into  this 
is  inserted  a  resistance  R  having  a  definite 
and  known  ratio  to  the  resistance  of  the  coil  C. 
According  to  this  ratio  more  or  less  of  the 
current  I  will  be  deflected  and  carried  through 
the  coil  of  the  instrument  by  means  of  the 
attachment  of  flexible  wires  to  the  terminals 
a  b  of  the  coil,  and  it  is  obvious  that  by 
changing  the  resistance  R  one  and  the  same 


DYNAMICS  157 

instrument  may  be  made  suitable  for  measur- 
ing currents  of  widely  different  magnitude.  The 
deflected  part  i  of  the  total  current  passes 
through  the  wires  of  the  coil,  and  those  parts 
of  the  winding  which  lie  parallel  to  the 
surface  of  the  cylindrical  armature  are  subject 
to  the  influence  of  the  induction  in  the  air 
space  between  armature  and  poles.  The 
dynamic  force  of  the  current  is  ~Bli,  where  I 
represents  the  total  length  of  wire  within  the 
air  space.  The  coil  will  thus  be  deflected 
against  the  controlling  force  of  the  spring, 
and  since  the  deflection  of  a  spring  is  pro- 
portional to  the  deflecting  force,  the  excursion 
of  the  pointer  over  the  scale  is  proportional 
to  the  current.  The  sense  in  which  the  pointer 
is  deflected  indicates  at  the  same  time  the 
direction  of  the  current. 

Up  to  the  present  we  have  considered  the 
dynamic  action  between  a  current  and  a 
magnetic  field,  but  we  have  still  to  consider 
the  dynamic  action  between  two  currents. 
For  this  purpose-  we  go  back  to  Biot-Savart's 
law  and  apply  it  to  the  case  of  a  very  long 
straight  conductor.  What  is  the  induction 
at  a  small  distance  a  from  the  axis  of  the 
wire  ?  This  problem  can  only  be  solved  by 
the  use  of  the  calculus,  and  therefore  it  must 


158  ELECTRICITY 

suffice  to  give  the  result.  It  is  this :  the 
force  on  unit  pole  placed  a  centimetres  from 
a  very  long  straight  wire,  through  which  the 
current  I  flows,  is  21  divided  by  a;  or  in 
symbols,  if  I  is  given  in  amperes 

R-     I2 

~10a 

If  we  have  two  wires  running  side  by  side 
each  lies  in  the  field  produced  by  the  other, 
and  thus  there  is  a  mechanical  force  drawing 
the  wires  together  if  the  currents  are  in  the 
same  direction,  and  forcing  them  apart  if 
the  currents  are  in  opposite  directions.  This 
is  the  explanation  of  the  experiment  de- 
scribed in  the  beginning  of  this  chapter. 
Let  us  now  inquire  as  to  the  magnitude  of 
this  force.  We  have  found 


and  inserting  the  value  of  B  we  obtain  the 
force  in  dynes 

F  — - 
or  per  meter  run 

F  =  |p  dynes. 


DYNAMICS 


159 


Two  wires,  each  carrying  100  amperes  and 
placed  one  cm.  apart,  will  exert  on  each 
other  a  force  of  only  20  grams  per  meter  run. 

The  relation  between  current  strength  in 
and  induction  round  a  long  straight  wire  may 
be  used  to  determine  for  any  configuration  of 
a  magnetic  system  the  exciting  force  in 


FIG.  9. 

ampere-turns  necessary  to  produce  a  desired 
magnetic  flux.  Let,  in  Fig.  9,  W  W  be  a 
portion  of  a  very  long  straight  wire,  through 
which  the  current  I  is  flowing.  Assume  at 
first  that  the  medium  surrounding  the  wire 
is  air,  and  imagine  a  ring  of  this  medium 
singled  out  for  consideration.  We  wish  to 
know  the  magnetic  flux  in  this  ring  of  mean 


160  ELECTRICITY 


radius  a  and  cross  section  A.     The  average 
induction  over  the 
the  flux  is  obviously 


21 

induction  over  the  cross   section  being  — , 


a 

To  carry  unit  pole  once  round  the  wire  along 
a  path  lying  within  the  ring  will  represent 
the  energy 

E  =  —  2na  =  4nl 
a 

since  energy  is  the  product  of  force  and 
distance  travelled. 

It  will  be  noticed  that  the  radius  of  the 
ring  does  not  appear  in  the  expression  for  the 
energy;  this  means  that  it  takes  exactly 
the  same  amount  of  energy  whether  we  carry 
the  unit  pole  round  the  wire  at  a  short  or  a 
long  radius.  All  we  have  to  be  careful  about 
is  that  we  go  once  completely  round  the 
wire  so  as  to  arrive  again  at  the  starting-point. 
Going  round  in  one  sense  costs  energy,  going 
round  in  the  other  sense  yields  energy. 
Obviously  the  two  amounts  must  be  equal, 
otherwise  we  would  have  a  perpetual  motion 
machine,  which  is  impossible.  For  the  same 
reason  it  is  not  even  necessary  that  the 


DYNAMICS  161 

journey  should  be  performed  in  a  circle 
concentric  with  the  wire;  any  path  costs 
or  yields  the  same  amount  of  energy. 

In  the  case  of  a  concentric  ring  of  uniform 
section,  in  which  the  average  induction  H  is 
produced  by  the  current  I,  we  have 


where  I  is  the  length  of  path.  The  magnetic 
force  acting  throughout  the  length  of  the 
ring  is  therefore 

„ 

T 

Let  us  now  replace  the  imaginary  ring  of 
air  by  a  real  ring  of  iron.  This  metal  being 
very  permeable  to  the  passage  of  magnetic 
lines  of  force,  we  shall  now  have  a  vastly 
greater  flux  within  the  ring.  The  magnet- 
ising force  is  as  before  4nl/l9  but  the  induction 
resulting  from  this  force  has  now  increased 
some  hundred,  or  thousandfold.  It  has  in- 
creased by  the  amount  corresponding  to  the 
coefficient  of  magnetic  permeability  ^.  We 
thus  get  the  mathematical  expression  for  the 
induction 


The  magnetising  force,  or  magnetic  force, 

L 


162  ELECTRICITY 


is  ~j~  and  the  induction  is  the  product  of 

magnetic  force  and  permeability.     The  equa- 
tion for  B  may  also  be  written  in  the  form 


This  is  the  same  expression  as  we  found  for 
a  ring  of  air,  but  with  this  difference,  that  the 
length  of  the  ring  instead  of  being  I  has  now 
shrunk  to  a  very  much  smaller  value,  namely 

—  .     If,  then,  we  have  a  ring  partly  consisting 

of  iron  and  partly  of  air,  we  may  consider 
the  whole  of  the  magnetic  circuit  as  consisting 
of  air,  but  we  must  reduce  the  length  of  the 
part  occupied  by  iron  in  the  ratio  of  //  to  /. 
To  illustrate  by  reference  to  Fig.  9.  Let  the 
iron  ring  be  interrupted  by  a  small  crevasse 
as  shown.  Let  the  length  of  the  ring  as  far 
as  it  consists  of  iron  be  119  and  let  the  width 
of  the  crevasse  or  air  gap  be  Z2.  The  length 
of  an  equivalent  ring  consisting  wholly  of 

air  will  then   be  ^  +  lz  and    the   induction 

will  be 

4:7*1 


DYNAMICS  163 

The  iron  surfaces  facing  each  other  across 
the  crevasse  are  the  polar  faces  of  an  electro- 
magnet excited  by  the  current  passing  through 
the  central  wire  W  W.  The  shape  of  the 
magnet  need  not  be  a  ring;  all  that  counts 
in  the  problem  is  the  length  of  the  path  in 
air  and  iron,  the  cross  section  of  the  magnetic 
circuit  and  the  permeability  of  the  particular 
iron  used.  In  Fig.  9  the  current  is  carried 
through  the  closed  magnetic  circuit  by  means 
of  a  very  long  straight  wire.  Needless  to 
say,  such  an  arrangement  is  quite  impractic- 
able. In  order  to  use  as  little  wire  as  possible 
we  must  wind  the  exciting  coil  close  over  the 
iron,  and  the  question  now  arises,  whether 
with  a  coil  of  any  form  wound  over  an  iron 
core  of  any  form,  the  relation  between 
magnetic  force  and  induction  still  holds  good. 

Let  us  first  assume  that  we  use  instead  of 
one  straight  and  very  long  wire  a  circular 
coil  of  many  turns.  This  is  shown  in  section 
in  Fig.  10.  If  all  the  n  wires  of  this  coil  were 
concentrated  in  one  circle  of  radius  R  the 
magnetic  force  in  the  centre  O  of  the  coil 
would  be 


As  we  move  to  either  side  of  O  this  force 


164 


ELECTRICITY 


very  rapidly  diminishes  according  to  a  certain 
mathematical  relation,  so  that  at  the  points 
A  and  B  it  is  already  inappreciable.  The 
question  we  have  to  answer  is  :  What  energy 
is  required  to  carry  unit  pole  from  a  point 
infinitely  distant  on  the  right  through  the 
coil  to  a  point  at  infinite  distance  on  the 


___    a_       .     A 


left  ?  The  mathematical  investigation  of  this 
problem  is  best  made  by  means  of  the  calculus, 
but  it  would  go  beyond  the  scope  of  this  book 
to  give  it  in  detail.  For  our  purpose  it  must 
suffice  to  note  the  result.  It  is  this  :  The 
energy  required  to  carry  unit  of  magnetic 
matter  once  through  the  coil  is  exactly  the 
same  as  that  required  to  carry  it  once  round 
an  infinitely  long  wire  in  which  the  same 
volume  of  current  flows  as  in  the  coil.  Thus 


DYNAMICS  165 

far  the  present  case  is  covered  by  the  previous 
argument.  But  we  do  not  want  to  carry  our 
unit  pole  from  infinity  on  the  right  to  infinity 
on  the  left;  we  want  to  carry  it  fairly  close 
round  the  coil,  say  along  the  dotted  line 
from  D  to  E  and  round  to  D  again.  The 
dotted  line  forms  the  closed  magnetic  path, 
whilst  the  coil  forms  the  electric  path,  both 
being  interlinked.  For  reasons  already  stated, 
the  exact  shape  of  the  path  is  immaterial.  As 
long  as  we  start  and  finish  the  journey  at  the 
same  point,  the  same  amount  of  energy  is  re- 
quired to  perform  it.  Let  us  then  make  the 
journey  in  the  following  way :  Go  from  D  a 
long  way  vertically  downwards.  This  part  of 
the  journey  costs  no  energy,  since  all  the  lines 
of  force  are  crossed  at  right  angles.  Then  go 
in  a  wide  sweep  to  A.  Also  this  part  of  the 
journey  costs  no  energy,  since  it  is  made  in 
a  region  where  there  is  no  force  at  all.  It  is 
only  when  we  travel  from  A  to  O  that  we 
get  into  a  region  where  we  encounter  opposing 
(or  helping)  forces.  By  passing  from  A 
through  O  to  B  we  expend  (or  recover)  the 
energy  represented  by  4^m,  whilst  the  journey 
from  B  to  D  is  again  performed  without 
recovery  or  expenditure  of  energy.  If,  then, 
the  dotted  line  represents  the  magnetic 


166  ELECTRICITY 

circuit  consisting  partly  of  iron  and  partly  of 
air  it  will,  as  regards  the  relation  between 
excitation  and  induction,  be  precisely  in  the 
same  position  as  is  the  crevassed  ring  in 
Fig.  9,  and  the  same  formulae  apply.  The 
excitation  produced  by  a  coil  may  be  con- 
veniently expressed  by  the  product  of  amperes 
and  turns,  or  "  ampere-  turns,"  and  then  we 
get  for  each  part  of  the  magnetic  circuit  a 
corresponding  portion  of  the  total  ampere- 
turns.  Let  AJ,  A2,  A3  be  the  cross  sections 
of  the  different  parts  of  the  magnetic  circuit, 
lv  Z2,  /3  the  corresponding  lengths,  pl9  ^2,  //3 
the  corresponding  permeabilities,  then  the 
ampere-turns  ni  necessary  to  produce  the 
flux  0  are  given  by  the  expression 


m= 


f  *i 


0-4  nlh 

This  formula  may  also  be  written  in  a 
manner  to  bring  in  the  induction  in  the  differ- 
ent parts  of  the  magnetic  circuit.  Remember- 
ing that  induction  is  flux  divided  by  cross 
section  we  have 


In    dynamo    machines,    one    part    of    the 
magnetic  circuit  is  air.     This  is  shown  in  the 


DYNAMICS 


167 


diagrammatic  sketch  of  part  of  a  dynamo, 
Fig.  11.  The  dotted  lines  represent  the  way 
the  lines  of  force  flow  between  field  magnet 
system  and  armature,  and  correspond  to  the 
dotted  line  E  D  E  in  Fig.  10.  The  hatched 
rectangles  represent  cross  section  through 
the  magnetising  coils  as  in  Fig.  10.  The 
physical  identity  between  the  real  machine 
and  the  theoretical  representation  of  the 


FIG.  11. 

interlinking  of  the  magnetic  and  electric 
circuits  as  represented  by  Fig.  10  will  be 
seen  at  a  glance.  For  air  ^  is  unity.  If  we 
call  B  the  induction  in  the  air  space  between 
armature  and  polar  faces,  and  I  the  combined 
length  of  the  two  air  spaces  that  lie  in  the 
path  of  the  magnetic  flux,  the  formula  for 
the  exciting  force  in  ampere-turns  becomes 

ni  =  0-8  El  +  ^?!  I,  +  2^5**,  + 

The  permeability  for  any  brand  of  iron  is 


168  ELECTRICITY 

not  a  constant,  but  depends  on  the  degree  to 
which  the  iron  is  magnetised.  In  such  iron 
as  is  used  in  the  construction  of  dynamo 
magnets  it  is  fairly  large  at  moderate  in- 
duction, but  becomes  very  much  reduced  at 
high  induction.  With  an  induction  of  about 
14,000  it  may  be  as  much  as  1,500,  whilst 
with  an  induction  of  20,000  it  may  be  as  low 
as  30  or  even  less.  It  is  convenient  to  repre- 
sent the  magnetic  quality  of  any  brand  of 
iron  by  a  so-called  "  magnetisation  curve," 
where  on  the  horizontal  axis  are  plotted  the 
ampere-turns  required  by  each  centimetre 
of  iron  path,  and  on  the  vertical  the  corre- 
sponding inductions.  By  using  such  curves  the 
above  formula  can  be  simplified  as  follows  —  • 


ni  =  0-8  El  +  X&  -f  xzlz  -f  /  .  . 

The  values  of  x  are  taken  from  the  magneti- 
sation curve  and  correspond  to  the  different 
values  of  the  induction  which  is  found  by 
dividing  the  flux  by  the  cross  section  of  the 
iron.  By  assuming  different  values  for  the 
total  flux  and  calculating  the  ampere-turns 
for  each  case,  we  get  a  series  of  co-ordinate 
values  of  ni  and  0,  which,  plotted  in  a  curve, 
characterise  the  machine  as  regards  its 
magnetisation.  Such  a  curve  is  therefore 


DYNAMICS 


169 


called  the  characteristic  of  magnetisation,  or 
the  magnetising  characteristic,  or  the  "  satura- 
tion curve  "  of  the  machine.  The  last  name 
is  not  a  very  happy  one,  since  there  is  no 
such  thing  as  absolute  saturation  of  a  magnetic 
circuit.  Moreover,  even  if  we  admit  that 
there  is  in  practice  a  saturation  point,  namely, 


flmpere  turns  per  pai 


FIG.  12. 

a  point  at  which  it  becomes  unprofitable  to 
increase  the  excitation  because  the  resulting 
increase  in  the  flux  is  insignificant,  the  term  is 
still  misleading,  because  a  machine  is  generally 
not  worked  at  this  so-called  saturation  point 
indicated  by  the  characteristic,  but  at  a  some- 
what lower  degree  of  magnetisation. 

Fig.  12  shows  the  general  type  of  such  a 
magnetisation  curve  and  also  approximately 
the  position  of  the  working  point. 


CHAPTER  VII 

THE    DYNAMIC    GENERATION    OF   ELECTRIC 
CURRENTS 

IN  the  previous  chapter  it  was  shown  that 
a  wire  placed  in  a  magnetic  field  will,  when 
traversed  by  a  current,  be  subject  to  a  force 
tending  to  displace  it  in  a  direction  which 
is  at  right  angles  both  to  the  axis  of  the  wire 
and  to  the  direction  of  the  lines  of  force.  An 
easy  way  for  finding  in  each  case  in  which 
direction  motion  will  be  produced  is  to  use 
the  left  hand  for  indicating  the  three  quantities 
concerned,  namely,  direction  of  the  magnetic 
force,  current  and  motion.  Set  thumb,  fore- 
finger and  middle  finger  at  right  angles  to 
each  other,  and  place  the  hand  so  that  the 
forefinger  points  in  the  direction  of  the  lines 
of  force,  and  the  central  finger  in  the  direction 
in  which  the  current  flows,  then  the  thumb 
will  indicate  in  which  direction  the  wire  will 
tend  to  displace  itself. 

If  the  displacement  is  allowed  to  take  place, 
170 


DYNAMIC   GENERATION         171 

it  will  be  under  the  influence  of  the  dynamic 
force  of  the  current,  and  since  force  producing 
motion  over  a  certain  distance  represents 
energy,  it  is  obvious  that  the  energy  repre- 
sented by  the  displacement  must  have  come 
from  the  current.  The  rate  at  which  the 
energy  is  produced,  that  is  the  energy  yielded 
up  by  the  moving  wire  in  unit  time,  is  called 
"  power,"  and  since  a  current  can  only  give 
up  power  if  it  flows  in  opposition  to  an  e.m.f .,  it 
follows  that  the  movement  of  the  wire  across 
the  lines  of  force  has  resulted  in  the  generation 
of  an  e.m.f.  in  such  a  direction  that  it  tends  to 
diminish  the  strength  of  the  current.  We  have 
here  another  example  of  Lenz's  law  mentioned 
on  p.  50.  To  maintain  the  current  at  its 
old  strength,  we  must  add  to  the  original 
e.m.f.,  which  was  required  to  overcome  merely 
the  ohmic  resistance  of  the  circuit,  a  further 
amount  of  e.m.f.  to  balance  the  opposing  e.m.f. 
caused  by  the  motion. 

The  direction  of  this  counter  e.m.f.,  or 
generally  of  any  e.m.f.  induced  by  the  motion 
of  a  conductor  in  a  magnetic  field,  may 
be  determined  by  using  the  right  hand  as 
an  indicator.  Put  thumb,  forefinger  and 
middle  finger  again  into  mutual  quadrature, 
and  place  the  hand  so  that  the  forefinger 


172  ELECTRICITY 

points  along  the  lines  of  force  and  the  thumb 
along  the  direction  of  motion,  then  the  central 
finger  will  indicate  the  direction  in  which  an 
e.m.f.  is  induced.  The  power  of  the  system 
represented  by  the  moving  wire  may  be  ex- 
pressed either  mechanically  as  the  product 
of  force  and  velocity,  or  electrically  as  the 
product  of  current  and  counter  e.m.f.  Both 
must  be  equal,  since  in  nature  power  can 
neither  be  created  nor  destroyed ;  it  can  only 
be  transformed.  By  equating  the  two  ex- 
pressions for  the  energy  we  obtain  the  relation 
between  the  mechanical  and  the  electrical 
unit  of  power.  Engineers  measure  power  in  a 
unit  called  the  horsepower,  electricians  measure 
it  in  a  unit  called  the  watt,  so  named  after 
James  Watt,  or  the  kilowatt,  which  means 
1000  watts.  Power  may,  however,  also  be 
expressed  in  dyne-centimetres,  or  "  ergs  "  per 
second,  which  is  the  way  of  expressing  it  in 
the  absolute  system  of  measurement.  Using 
for  the  moment  this  system,  we  have  the 
equation  between  mechanical  and  electrical 
power— 

Fv  =  JE,  where  v  is  velocity, 
and  since  F  =  B/J, 

we  have  also  BlJv  =  JE, 

and  from  this  we  find  the  law  determining  the 


DYNAMIC   GENERATION         173 

magnitude  of  the  e.m.f.  generated  by  electro- 
magnetic induction.     It  is 


The  absolute  unit  of  e.m.f.  is  that  e.m.f.  which  is 
generated  in  a  wire  one  centimetre  long,  when 
moved  with  a  velocity  of  one  centimetre  per 
second  at  right  angles  across  the  lines  of  a 
magnetic  field  in  which  the  induction  is  one 
electromagnetic  unit.  The  unit  of  e.m.f.  thus 
defined  is  inconveniently  small  for  practical 
work.  A  much  larger  unit,  namely  the 
"volt,"  is  used  in  practice,  and  its  magnitude 
is  100,000,000  =  108  as  large.  On  the  other 
hand,  the  electromagnetic  unit  of  current  is 
10  times  as  large  as  the  practical  unit,  namely 
the  ampere.  If,  then,  we  wish  to  pass  from 
the  absolute  system  of  measurement  of  power 
to  the  practical  system,  we  must  use  the 
reducing  factor  100,000,000  divided  by  10, 
or  10,000,000  =  107.  We  thus  find  that  the 
power  represented  by  10  million  dyne-centi- 
metres per  second  is  equal  to  the  power  repre- 
sented by  one  watt.  The  energy  represented 
by  10  million  ergs  is  equal  to  the  energy  repre- 
sented by  one  watt  second  or  one  "  Toule." 

A   similar   reduction   can   be   made   when 
passing  from  the  absolute  system  of  power 


174  ELECTRICITY 

measurement  to  the  practical  system  used 
by  mechanical  engineers.  The  kilogram  is 
equivalent  to  981,000  dynes,  and  one  kilogram- 
metre  is  represented  by  98,100,000  ergs.  To 
produce  10,000,000  ergs,  which  is  equivalent 

to  one  watt  second,  only  (~~  =  0-102  kgm. 

i/O    1 

of  mechanical  energy  is  required;  or  one 
kgm.  per  second  of  mechanical  power  is  the 
same  as  9-81  watts  of  electrical  power.  Since 
the  English  horsepower  is  550  ft.-lb.  per 
second,  or  76  kgm.  per  second,  the  electrical 
equivalent  of  one  hp.  is  746  watts.  The 
output  of  electric  motors  is  generally  stated 
in  hp.,  that  of  electric  generators  in  kw. 

The  discovery  of  electromagnetic  induction 
as  a  source  of  current  is  due  to  Faraday.  He 
first  enunciated  the  fundamental  fact  that 
if  a  wire  cuts  across  lines  of  magnetic  force, 
an  e.m.f .  is  induced  in  the  wire.  This  e.m.f .  will 
produce  a  current,  if  the  ends  of  the  wire  are 
joined  up  by  some  other  conductor.  We  have 
thus  a  closed  electric  circuit,  of  which  a 
particular  part,  namely  the  wire  under  con- 
sideration, is  cutting  through  lines  of  force; 
and  we  also  have  a  magnetic  circuit  inter- 
linked with  the  electric  circuit.  That  inter- 
linking must  take  place  is  obvious.  As  long 


DYNAMIC   GENERATION         175 

as  there  is  any  cutting  of  lines,  some  lines  must 
be  inside  and  some  outside  the  electric  circuit  ; 
in  fact  the  cutting  is  necessarily  accompanied 
by  the  transfer  of  lines  from  the  outside  to  the 
inside  of  the  electric  circuit  or  vice  versa. 
Further,  lines  of  force  must  be  conceived  as 
curves  closed  in  themselves,  and  therefore  all 
the  lines  passing  inside  the  electric  circuit  form 
a  kind  of  magnetic  ring  which  is  interlinked 
with  the  ring  formed  by  the  electric  circuit. 
If,  then,  the  wire  cuts  through  some  of  these 
lines,  the  amount  of  interlinkage  is  altered,  and 
we  may  thus  also  define  the  electromagnetic 
induction  of  an  e.m.f.  as  a  process  of  altering 
the  interlinkage  of  the  two  circuits.  In  the 
expression  for  E  given  above,  namely  — 


the  product  of  induction,  length  of  conductor 
and  velocity  is  obviously  nothing  else  than  the 
magnetic  flux  added  to  or  withdrawn  from  the 
electric  circuit  in  unit  time,  that  is  the  rate 
at  which  the  interlinked  flux  changes  with 
time.  We  may,  therefore,  also  write  for  the 
e.m.f.  in  absolute  units  produced  in  a  coil  of  one 
turn  — 


176 


ELECTRICITY 


d0  being  the  very  small  change  of  flux  that 
occurs  in  the  very  small  time  dt. 

If  the  coil  has  n  turns  the  e*m.f .  induced  will 


FIG.  13. 


be  n  times  as  great,  and  its  value  expressed  in 
volts  will  be  — 


That  an  e.m.f.  is  produced  by  the  change  of 
flux  passing  through  a  coil  was  proved  experi- 
mentally by  Faraday  in  the  following  way. 
Fig.  13  represents  a  permanent  horseshoe 
magnet  securely  fastened  to  the  table.  Its 
armature  or  keeper  of  soft  iron  is  provided  with 
a  coil  of  many  turns  of  fine  wire.  One  end  of 


DYNAMIC  GENERATION         177 

this  coil  is  furnished  with  a  little  metal  plate, 
and  the  other  end  of  the  wire  rests  loosely  on 
this  plate.  If  the  keeper  is  placed  over  the 
poles,  the  flux  emanating  from  them  passes 
through  the  coil.  If  the  keeper  is  taken  away, 
the  lines  which  previously  passed  through  its 
interior  vanish.  By  drawing  the  keeper  away 
slowly  the  rate  at  which  the  lines  vanish  is 
slow,  and  consequently  no  very  great  e.m.f. 
will  be  induced  in  the  coil,  but  if  we  accelerate 
this  rate  a  fairly  high  e.m.f.  may  be  induced. 
In  order  that  it  may  be  possible  to  tear  off 
the  keeper  very  quickly,  it  is  provided  with 
handles.  By  giving  these  handles  a  blow  with 
both  hands  from  below,  the  keeper  comes  off 
with  a  jerk,  and  the  rate  at  which  the  flux 
diminishes  is  great,  hence  a  large  e.m.f.  is 
induced.  At  the  same  time,  as  a  consequence 
of  the  jerky  motion,  the  point  of  the  loose  wire 
resting  on  the  plate  is  caused  to  separate  a 
little  and  thus  an  arc  is  produced  as  evidence 
that  a  current  is  circulating  through  the  coil. 
Some  of  the  ignition  apparatus  used  in  motor 
cars  and  some  mine  exploders  are  constructed 
on  the  same  principle.  Faraday's  plate  and 
loose  wire  are  replaced  by  a  properly  con- 
structed sparking  plug,  but  the  spark  is  pro- 
duced in  the  same  way  as  in  the  original 
M 


178  ELECTRICITY 

experiment,  namely,  by  the  sudden  change 
of  flux  through  a  coil,  the  terminals  of  which 
are  connected  to  the  plug.  Electromagnetic 
induction  is  also  the  working  principle  of  all 
dynamo  machines,  but  here  we  do  not  want 
to  produce  sparks  at  given  times,  but  a  sus- 
tained electric  current  flowing  under  a  definite 
and  steadily  maintained  e.m.f.  Hence  coils 
must  go  into  and  come  out  of  action  in  regular 
rotation,  and  this  condition  is  fulfilled  by  the 
part  in  the  dynamo  called  the  armature. 

Let,  in  Fig.  14,  A  be  a  cylindrical  piece  of 
iron  capable  of  revolving  between  the  poles 
N  S;  and  let  this  cylinder  be  wound  with  a 
coil  Cp  C2,  the  wires  passing  across  the  face 
and  along  the  sides  of  the  cylinder.  One 
end  of  this  coil  is  attached  to  an  insulated 
metal  ring  R1,  and  the  other  to  a  similar  ring 
R2.  Metal  springs  Bx  and  B2,  technically 
termed  "  brushes,"  press  against  these  rings 
for  the  purpose  of  maintaining  electrical 
continuity  between  the  revolving  coil  and  the 
fixed  points  of  attachment  of  the  external 
circuit,  which  by  way  of  example  we  may  take 
to  contain  an  incandescent  lamp.  In  the 
position  shown,  the  full  flux  from  the  magnets 
passes  through  the  coil,  but  no  e.m.f.  is 
generated,  because  at  that  particular  moment 


DYNAMIC  GENERATION         179 

there  is  no  change  in  the  flux  if  the  armature 
is  slightly  rotated  to  one  side  or  the  other.  In 
other  words,  the  rate  of  change  of  flux  through 
the  coil  is  zero.  Now  imagine  the  armature 


FIG.  14. 

revolving  clockwise,  so  that  the  side  of  the 
coil  marked  Ca  comes  opposite  the  N  pole. 
Now  the  rate  at  which  the  lines  of  force 
emanating  from  that  pole  are  cut  is  a  maxi- 
mum, and  at  the  same  time  the  flux  through 
the  coil  is  zero.  At  that  moment  a  maximum 
of  e.m.f.  is  induced  in  the  wires  of  the  coil  on 


180  ELECTRICITY 

both  sides.  By  the  right-hand  rule  stated 
on  p.  171  we  find  that  in  the  wires  Cx  the 
direction  of  the  e.m.f.  will  be  downwards,  or 
away  from  the  observer,  whilst  in  the  wires 
C2  it  will  be  upwards,  or  towards  the  observer. 
Both  these  actions  combined  produce  a 
potential  difference  between  the  rings  R1? 
R2,  with  the  result  that  at  that  moment  the 
strength  of  the  current  flowing  through  the 
lamp  will  be  a  maximum.  As  the  rotation 
proceeds,  the  e.m.f.,  and  with  it  the  current, 
will  diminish  until,  when  the  vertical  position 
of  the  coil  has  once  more  been  reached,  the 
e.m.f.  will  again  be  zero.  Now  the  wires 
Cj  occupy  the  position  which  formerly  was 
occupied  by  the  wires  C2,  but  owing  to  this 
reversal  of  position  the  current  which  now 
starts,  flows  in  the  opposite  direction.  The 
lamp  thus  receives  alternately  current  in 
one  and  the  opposite  direction;  it  is  lighted 
with  an  alternating  current.  We  have  here 
a  simple  form  of  dynamo  machine  producing 
alternating  current.  The  rate  at  which  the 
direction  of  the  current  alternates  is  technically 
termed  the  "  frequency."  In  a  machine 
having  two  poles  it  coincides  with  the  numbers 
of  complete  revolutions  performed  in  one 
second. 


DYNAMIC  GENERATION         181 

Twice  during  each  complete  period  the  lamp 
receives  alternately  a  maximum  of  current 
and  no  current  at  all.  Will  this  produce  a  dis- 
agreeable flicker  ?  The  answer  to  this  question 
depends  on  two  things;  first  the  frequency 
and  then  the  thermal  storage  capacity 
of  the  lamp  filament.  The  light  is  due  to 
the  high  temperature  of  the  metallic  filament, 
and  that  is  due  to  the  current.  A  strong 
current  produces  more  light  than  a  weak  one, 
but  the  emission  of  light  does  not  instantly 
follow  the  variation  in  current  strength. 
Time  is  required  for  heating  and  for  cooling, 
and  provided  the  intervals  between  heating 
are  sufficiently  short  as  compared  to  the  heat 
which  the  lamp  can  radiate  in  the  time,  its 
temperature  will  not  materially  change  and 
there  will  be  no  flicker.  Obviously  the  thinner 
the  filament  and  the  greater  its  radiating 
power,  the  higher  must  be  the  frequency 
at  which  flickering  is  no  longer  noticeable. 
There  is  also  a  personal  element  in  the 
observation  of  flickering;  some  persons 
observe  it  sooner  and  feel  it  more  unpleasantly 
than  others.  From  experiments  I  have  made 
with  various  lamps  and  assisted  by  various 
observers,  I  found  that  at  a  frequency  of  25 
no  observer  could  detect  flickering  when 


182  ELECTRICITY 

carbon  lamps  were  tried,  but  some  detected, 
or  thought  they  detected,  flickering  when 
metallic  filament  lamps  were  tried.  At 
slightly  less  than  25  frequency  the  majority 
of  observers  detected  flickering.  We  may 
thus  take  25  as  a  yet  permissible  lower  limit 
for  the  frequency  if  the  current  is  to  be  used 
in  incandescent  lighting.  With  arc  lighting 
the  lowest  frequency  permissible  is  40.  As  a 
general  rule  lighting  current  is  supplied  at  a 
frequency  of  50.  To  get  such  a  frequency 
with  a  machine  built  on  the  principles  shown 
in  Fig.  14  would  require  driving  it  at  a  speed 
of  3000  revolutions  a  minute.  Such  a  speed 
is  too  high  for  ordinary  steam  engines,  athough 
it  is  well  within  the  range  of  steam  turbines. 
Apart,  however,  from  the  question  of  driving, 
it  is  mechanically  and  electrically  wrong  to 
subject  a  coil,  which  must  be  highly  insulated, 
to  so  high  a  speed.  High  speed  means  great 
centrifugal  forces,  and  that  means  great 
mechanical  stress  on  the  insulating  material. 
Such  stresses  should  be  avoided  as  far  as 
possible.  For  this  reason  the  mechanical 
arrangement  of  field  magnet  and  armature 
is  reversed  in  modern  machines.  It  is  the 
magnetic  field  which  is  caused  to  rotate,  and 
then  it  is  possible  to  keep  the  armature 


DYNAMIC  GENERATION 


183 


stationary.  The  objection  against  rotating 
coils  does  not  apply  to  the  exciting  coils  of 
the  field  magnet  system  with  anything  like 
the  same  weight  as  to  the  armature  winding. 
In  the  first  place,  the  field  coils  need  only  be 
insulated  for  some  hundreds,  but  not  thousands 
of  volts,  and  in  the  second  place  they  can  be 


FIG.  15. 


made  of  a  very  compact  and  simple  shape,  and 
this  renders  a  safe  mechanical  attachment 
possible. 

Fig.  15  shows  diagrammatically  the  general 
principles  on  which  modern  alternating  current 
dynamos  are  constructed.  The  coils  in  which 
the  alternating  e.m.f.  is  generated  are  carried 
on  the  inner  surface  of  a  cylindrical  armature, 
technically  termed  the  "  stator  "  because  it 
is  a  fixed  part.  The  magnet  system  is  the 


184  ELECTRICITY 

revolving  part  or  "  rotor,"  and  may  have 
two  or  any  even  number  of  poles.  In  Fig.  15 
it  is  assumed  that  the  rotor  is  multipolar,  so 
that  the  desired  frequency  may  be  obtained 
with  a  moderate  speed  of  revolution.  The 
action  of  the  machine  is  the  same  as  already 
explained  with  reference  to  Fig.  14.  In  the 
position  shown  the  polar  faces  are  opposite 
the  sides  of  the  coils,  no  flux  is  going  through 
the  coils,  but  the  rate  of  change  of  flux  is 
a  maximum.  All  the  active  wires  on  the  face 
of  the  armature  are  being  cut  by  lines  of 
force,  and  the  e.m.f.  has  maximum,  or  crest 
value.  The  term  crest  value  is  chosen  to 
indicate  the  wavy  or  undulatory  character  of 
the  current. 

If  the  stator  were  made  of  solid  iron,  an 
e.m.f.  would  be  induced  not  only  in  the  wires, 
where  we  desire  to  have  it,  but  also  in  the 
mass  of  the  iron,  where  we  do  not  desire  it. 
We  do  not  desire  to  have  currents  flowing  in 
the  body  of  the  stator  iron,  because  whenever 
a  current  flows  through  a  conductor,  be  it  a 
wire  or  a  lump  of  iron,  the  material  of  the 
conductor  gets  heated,  and  that  heat  has  to 
be  paid  for  in  the  shape  of  some  extra  power 
which  the  driving  engine  is  called  on  to  supply. 
This  would  be  pure  waste,  and  to  avoid  such 


DYNAMIC  GENERATION         185 

waste  taking  place,  it  is  necessary  to  prevent 
currents  circulating  in  the  mass  of  the  stator 
iron. 

We  cannot  avoid  an  e.m.f.  being  generated 
in  the  iron  as  well  as  in  the  copper  conductors, 
since  both  are  side  by  side;  but  we  can  pre- 
vent this  e.m.f.  from  producing  a  current,  and 
this  is  done  by  interrupting  its  path.  This 
means  subdividing  the  iron  into  thin  plates, 
which  are  insulated  from  each  other  by  varnish 
or  paper.  This  does  not  interfere  with  the 
flow  of  magnetism,  for,  as  we  have  seen,  there 
is  always  quadrature,  that  is,  a  right-angular 
relation  between  flux  and  the  direction  in 
which  an  e.m.f.  is  induced.  Hence  an  insula- 
ting surface  which  interrupts  electrical  con- 
tinuity is  parallel  to  the  direction  of  the 
magnetic  flux,  and  apart  from  slightly  re- 
ducing the  available  cross  section  for  the 
transmission  of  the  lines  of  force,  does  not 
interfere  with  the  magnetic  circuit.  It  may 
be  mentioned  that  not  only  in  such  dynamos, 
but  in  all  electrical  machinery  and  apparatus 
where  there  is  either  a  change  of  flux  or  a 
progression  of  flux  through  iron,  the  iron  must 
be  laminated. 

It  has  been  shown  in  the  previous  chapter 
that  very  considerable  forces  act  on  armature 


186  ELECTRICITY 

wires.  Their  safe  mechanical  support  thus 
becomes  a  matter  of  first  importance.  We 
cannot  stick  the  wires  on  the  very  surface  of 
the  armature,  but  we  can  place  them  into 
slots  or  tunnels  close  to  the  surface.  In  this 
way  the  wires  are  securely  held  and  are 
relieved  from  mechanical  stress,  which  is 
now  taken  by  the  iron  bridges  between  the 
wires  and  not  by  the  wires  themselves.  The 
slots  or  tunnels  are  lined  with  tubes  of  in- 
sulating material,  and  thus  complete  protec- 
tion of  the  winding,  both  in  a  mechanical 
and  electrical  sense,  is  secured. 

It  will  be  noticed  that  in  the  alternator 
diagrammatically  shown  in  Fig.  15  more  than 
half  the  inner  surface  of  the  stator  is  left 
free  from  winding.  This  free  space  may  be 
utilised  for  a  second  winding  placed  exactly 
midway  into  the  free  space  left  by  the  first 
winding.  Let  us  call  the  two  systems  of 
winding  A  and  B.  If  the  poles  are  in  such  a 
position  that  the  e.m.f.  in  the  A  winding  is 
zero,  they  are  exactly  opposite  the  wires  of 
the  B  winding,  and  generate  in  these  wires 
crest  value  of  e.m.f.  Conversely  if,  a  moment 
later,  the  e.m.f.  of  the  B  winding  is  zero,  that 
of  the  A  winding  has  crest  value.  We  have 
thus  two  waves  of  e.m.f.  and  current  running 


DYNAMIC  GENERATION        187 

through  the  machine.  These  waves  are  rela- 
tively to  each  other  displaced  by  a  quarter 
period.  A  machine  of  this  kind,  which  from 
the  same  armature  gives  two  independent 
currents  displaced  by  a  quarter  period,  is 
called  a  "  two-phaser "  or  a  "  two-phase 
machine."  We  may  also  provide  the  arma- 
ture with  three  distinct  phase  windings,  each 
displaced  against  the  others  by  one-third 
of  a  full  period,  or  120  degrees.  Such  a 
machine  is  called  a  "  three-phaser "  or 
"  three-phase  machine."  The  use  of  three- 
phase  current  results  in  certain  technical 
and  financial  advantages  in  the  supply  of 
electricity,  and  it  is  on  this  account  that  most 
modern  electricity  works,  if  they  use  alternat- 
ing current  at  all,  use  it  in  the  shape  of  three- 
phase  current. 

But  suppose  an  electricity  works  does  not 
want  to  supply  alternating  current  to  its 
customers,  but  continuous  current.  What 
sort  of  machinery  will  it  have  to  use  in  this 
case  ?  If  we  wish  to  produce  continuous, 
that  is  uni-directed,  current  by  electromagnetic 
induction,  we  must  obviously  add  to  our 
machine  some  organ  which  reverses  the  current 
in  every  second  half -wave.  But  this  is  not 
enough.  Even  after  we  have  reversed  every 


188  ELECTRICITY 

second  half -wave,  the  current  will  be  pulsating 
between  zero  and  a  maximum.  It  is  true, 
the  maximum  will  always  have  the  same  sign 
corresponding  with  the  general  sense  of  flow, 
but  the  flow  will  be  extremely  irregular,  and 
in  some  respects,  such  as  the  question  of 
flickering,  no  better  than  an  alternating 
current.  The  alteration  we  need  make  to 
get  out  of  the  machine  shown  in  Fig.  14  a 
uni-directed  current,  or,  as  it  is  technically 
termed,  a  "  direct  current "  (abbreviation 
"  DC  "),  is  simple  enough.  We  need  only,  as 
shown  in  Fig.  16,  replace  the  two  whole  rings 
by  one  ring  split  into  two  halves  Rx  R2,  which 
are  insulated  from  each  other  and  connected 
respectively  to  the  two  ends  of  the  coil.  In 
Fig.  16  the  coil  is  shown  as  consisting  of  only  a 
single  turn.  This  is  done  to  avoid  a  compli- 
cated diagram.  In  reality  the  coil  would  have 
a  large  number  of  turns.  The  brushes  are 
placed  right  and  left  on  a  horizontal  diameter. 
By  applying  the  right-hand  rule  it  will  be 
seen  that  with  clockwise  rotation  of  the 
armature,  brush  ^  is  always  the  negative 
and  B2  always  the  positive  brush.  The 
machine  therefore  gives  DC,  but  a  strongly 
pulsating  DC. 
In  order  to  smooth  out  the  pulsation  to  an 


DYNAMIC  GENERATION 


189 


extent  which  will  make  the  current  really 
continuous,  a  special  method  of  arranging 
the  winding  and  a  special  organ,  namely  the 
"  commutator,"  is  required.  In  a  sense  the 
two  half -rings  of  Fig.  16  are  a  commutator, 
for  they  are  instrumental  in  commutating  the 


AC  into  a  pulsating  DC.  But  this  commutator 
has  only  two  segments,  hence  its  imperfect 
action.  The  merit  of  having  improved  both 
method  of  winding  and  commutator,  so  that 
the  machine  may  give  a  steady  DC,  belongs 
to  Pacinotti,  who  was  Professor  of  Physics 
in  the  Turin  University.  He  published  in 
1864  a  description  of  a  continuous  current 
dynamo  machine,  which  he  had  constructed 


190  ELECTRICITY 

four  years  previously  for  purely  scientific 
laboratory  experiments.  The  organ  in  which 
the  continuous  current  was  generated,  con- 
sisted of  an  iron  ring  provided  with  a  winding 
of  copper  wire  in  the  form  of  a  continuous 
spiral  closed  in  itself.  At  even  intervals 
connections  were  brought  out  from  this  spiral 
to  the  segments  of  a  commutator.  By 
adopting  a  commutator  with  many  segments 
instead  of  the  two  segments  of  Fig.  16,  the 
current  loses  most  of  its  pulsating  character, 
and  becomes  practically  a  continuous,  evenly 
flowing  current. 

It  is  curious  to  note  that  Pacinotti, 
although  he  was  the  first  inventor  of  the 
modern  method  of  winding  DC  armatures, 
does  not  seem  to  have  realised  the  im- 
mense practical  importance  of  his  invention; 
at  any  rate  he  made  no  attempt  to  utilise  it 
practically.  In  this  respect  there  is  some 
similarity  between  Pacinotti  and  another 
great  Italian  physicist,  namely  Galileo 
Ferraris,  who  in  1887  discovered  a  method  by 
which  rotative  motion  could  be  obtained  by 
the  combined  action  of  two -phase  or  three- 
phase  currents.  Ferraris  not  only  failed  to 
see  the  importance  of  his  discovery  for  the 
production  of  motive  power,  but  he  went  even 


DYNAMIC  GENERATION         191 

so  far  as  to  throw  doubt  upon  it;  for  in  his 
first  publication  he  said  that  his  discovery 
might  possibly  have  some  use  in  the  construc- 
tion of  electricity  meters,  but  that  it  would 
probably  be  useless  for  electric  motors.  Yet 
more  than  half  the  motive  power  produced 
electrically  nowadays  is  produced  in  machines 
in  which  the  discovery  made  by  Ferraris  is 
utilised.  Pacinotti  was  content  to  utilise 
his  invention  for  his  own  scientific  experi- 
ments, but  he  did  not  apply  it  for  industrial 
purposes.  This  was  done  by  Zenobe  Theophil 
Gramme  in  1869.  It  is  very  probable  that 
Gramme,  who  at  the  time  was  employed  as 
pattern-maker  in  an  electrical  manufacturing 
firm,  had  never  heard  of  Pacinotti's  invention. 
He  re-invented  the  spiral  winding  and  the 
many-part  commutator;  and  recognising  the 
practical  importance  of  this  invention  he 
patented  it  in  1869.  Hence  this  type  of 
armature  winding  is  called  a  "  Gramme 
winding,"  or  also  a  "  Gramme  Ring  "  or  a 
"  Ring  Winding."  It  is  diagrammatically  re- 
presented in  Fig.  17.  S  N  are  the  poles  of 
the  field-magnet  system  so  shaped  as  to  pro- 
duce a  polar  cavity  in  which  the  armature 
revolves.  This  consists  of  an  iron  ring  R 
wound  with  insulated  copper  wire,  the  winding 


192 


ELECTRICITY 


forming  a  spiral,  Sp,  closed  in  itself.  At 
even  intervals  this  winding  is  tapped  by 
conductors  which  connect  it  to  the  segments 
of  the  commutator  C.  Let  the  armature 
revolve  clockwise,  as  shown  by  the  arrow. 
If  the  reader  will  apply  the  right-hand  rule 


FIG.  17. 

given  on  p.  171  he  will  find  that  in  all 
those  parts  of  the  continuous  spiral,  which 
lie  immediately  under  the  N  pole  at  any 
moment,  an  e.m.f.  directed  as  shown  by  the 
arrows  will  be  generated.  The  same  applies 
to  those  parts  of  the  spiral  which  lie  within 
the  sphere  of  influence  of  the  S  pole.  By 
following  the  winding  in  the  direction  of 


DYNAMIC   GENERATION         193 

these  arrows  we  find  that  these  e.m.f.  impulses 
all  add  up  in  the  right  sense,  so  as  to  push 
current  out  at  the  positive  brush  B  shown  at 
the  top ;  and  to  draw  current  into  the  arma- 
ture at  the  negative  brush  B  shown  at  the 
bottom  of  the  figure.  By  joining  these 
brushes  to  the  terminals  of  some  external 
circuit,  a  continuous  current  in  this  circuit 
is  therefore  obtained. 

It  should  be  noted  that  only  those 
portions  of  the  wire  which  are  between  the 
ring  and  the  poles  are  active.  Those 
parts  of  the  wire  which  pass  through  the 
inside  of  the  ring  contribute  nothing  to  the 
generation  of  an  e.m.f.,  because  the  ring 
itself  shields  them  from  the  influence  of  the 
poles ;  and  if  this  shielding  were  not  present, 
the  influence  would  be  the  wrong  way.  Thus 
the  inside  part  of  the  spiral  is  useless  and 
even  harmful,  for  it  increases  the  resistance 
and  it  magnetises  the  inside  of  the  ring.  This 
magnetisation,  being  at  right  angles  to  the 
magnetisation  originally  produced  by  the 
field  magnets,  does  not  directly  interfere  with 
the  working  of  the  machine,  but  it  has  an 
indirect  influence.  The  shaft  and  the  attach- 
ment of  the  ring  to  it  must  be  of  metal,  and 
this  metal,  in  cutting  through  the  lines  of 

N 


194  ELECTRICITY 

force  of  the  internal  field,  becomes  itself  the 
seat  of  e.m.f.'s  which  produce  what  may  be 
called  parasitic,  that  is  useless,  currents  in 
these  metal  masses,  producing  heat  and  wast- 
ing power.  The  mechanical  attachment  be- 
tween ring  and  shaft  is  also  difficult,  as  the 
space  is  limited  and  most  of  it  is  wanted 
for  the  accommodation  of  the  winding  itself. 
All  these  difficulties  would  vanish  if  it  were 
possible  to  avoid  passing  the  wire  through  the 
interior  of  the  ring.  In  this  case  we  need 
not  use  a  ring  at  all,  but  we  might  use  a 
solid  drum,  or  at  least  a  drum  of  iron  made 
up  of  thin  plates,  but  filling  as  much  of 
the  space  as  may  be  necessary  to  carry  the 
magnetic  flux  across  from  one  pole-piece  to 
the  other. 

It  is  the  merit  of  a  German  engineer, 
namely  von  Hefner  Alteneck,  to  have  made 
these  improvements  possible  by  the  invention 
of  what  is  technically  known  as  "  drum 
winding."  The  wires  are  left  on  the  outside 
of  the  ring  as  shown  in  Fig.  17,  but  instead  of 
taking  the  second  half  of  each  turn  through 
the  ring,  it  is  taken  across  the  end  face  of  the 
drum  and  then  down  its  outer  surface.  The 
connections  to  the  commutator  are  tapped 
off  from  every  second  wire.  Thus  a  drum 


DYNAMIC  GENERATION         195 

containing  100  wires  would  have  a  50  part 
commutator,  and  every  second  wire  would  be 
connected  to  this  commutator.  Instead  of 
single  wires,  groups  of  wires  made  up  into 
coils  may  be  used.  It  will  be  obvious  that 
the  e.m.f.  generated  in  the  armature  will  be 
the  greater  the  greater  the  number  of  wires 
on  the  drum.  If  then  a  high  e.m.f.  is  required, 
the  number  of  wires,  counted  all  round  the 
armature,  may  easily  become  so  great,  that 
if  we  have  to  provide  a  segment  in  the  com- 
mutator for  every  second  wire,  the  commuta- 
tor would  have  to  be  made  up  of  exceedingly 
thin  segments.  For  obvious  reasons  there  is  a 
limit  to  the  decrease  in  the  thickness  of 
commutator  segments,  so  that  the  rule,  that 
one  segment  must  be  provided  for  every  two 
wires,  cannot  always  be  adhered  to.  This 
difficulty  may  be  overcome  by  grouping  the 
wires  in  coils.  The  number  of  segments  need 
then  only  be  as  large  as  the  number  of  coils, 
that  is  one  half  the  number  of  coil  sides. 
Each  coil  side  then  takes  the  place  of  one 
individual  wire. 

There  is  in  connection  with  drum  winding 
a  purely  mechanical  difficulty  which  must  be 
mentioned.  I  said  above  that  the  connection 
between  the  front  end  of  one  wire  to  the  front 


196  ELECTRICITY 

end  of  the  wire  diametrically  opposite  is 
taken  across  the  face  of  the  drum.  It  is 
obviously  impossible  to  take  it  straight 
across,  for  on  the  one  side  there  is  the  shaft 
in  the  way  and  on  the  other  the  commutator, 
the  diameter  of  which  may  be  half  that  of 
the  drum  or  even  more.  Thus  the  space  at 
both  drum-heads  is  not  free,  and  to  take  the 
connections  across  we  must  so  shape  them  as 
to  avoid  these  central  obstructions  and  at 
the  same  time  not  interfere  with  each  other. 
This  is  a  purely  mechanical  problem,  and  has 
been  solved  in  various  ways.  As  it  has  only 
interest  for  the  professional  designer  of 
dynamos  the  various  solutions  need  not  be 
detailed  here,  but  it  may  be  pointed  out  that 
the  mechanical  difficulties  of  arranging  the 
end  connections  become  less  serious  when 
drum  winding  is  applied  to  a  machine  having 
more  than  two  poles.  In  a  four-pole  machine 
the  end  connection  need  only  span  a  quarter 
of  the  circumference ;  and  in  a  six-pole  machine 
only  one- sixth.  Thus  to  avoid  commutator 
and  shaft  is  an  easy  matter,  whilst  avoiding 
mutual  interference  of  end  connections  is 
also  easier,  since  their  length  is  reduced  and 
there  are  fewer  of  them  crossing  each  other. 
This  is  one  of  the  reasons  why  modern 


DYNAMIC  GENERATION         197 

machines  are  generally  made  with  four  or 
more  poles. 

Another  feature  of  modern  machines  is  the 
secure  fastening  of  the  active  wires.  Fig.  17 
is  merely  a  diagrammatic  representation  to 
illustrate  a  principle;  it  is  not  a  drawing 
of  a  real  machine.  If  the  wire  were  simply 
wound  over  the  outside  of  a  smooth  drum  it 
would  be  very  difficult  to  hold  it  securely  in 
place.  Not  only  would  the  wire  bulge  out 


FIG.  18. 

by  reason  of  centrifugal  force,  but  the 
magnetic  drag  on  the  wire  would  displace 
it  along  the  circumference.  In  modern 
machines  the  wires  or  coil  sides,  as  the  case 
may  be,  are  secured  in  position  by  being 
placed  in  slots,  as  shown  in  Fig.  18.  The 
core  of  the  armature  consists  of  thin  iron 
plates  which  are  slotted  on  special  stamping 
machines.  In  building  up  the  core,  the  plates 
are  so  laid  one  upon  the  other  that  all  the 
slots  register  properly  and  form  grooves 
parallel  to  the  axis*  into  which v  the  wires  are 


198  ELECTRICITY 

placed.  To  prevent  the  wires  from  being 
thrown  out  by  the  action  of  centrifugal  force 
the  groove  is  closed  by  the  insertion  of  dove- 
tailed wooden  wedges.  The  reason  for  using 
thin  plates  instead  of  a  solid  body  for  the 
core  of  the  armature  is  to  prevent  the  creation 
of  parasitic  currents  in  the  mass  of  the  iron. 
This  point  has  already  been  discussed  earlier 
in  this  chapter  when  dealing  with  alternating 
current  machines,  and  the  reasoning  then 
applied  remains  valid  also  for  D  C  machines. 
When  explaining  the  action  of  an  armature 
with  closed  winding,  we  assumed  the  exist- 
ence of  a  magnetic  field  emanating  from  the 
poles  N  S  without  specifying  how  this  field 
is  produced.  We  might  produce  it  by  using 
some  source  of  electricity  such  as  a  primary 
or  a  storage  battery  to  excite  the  field  magnets, 
but  this  would  be  a  cumbersome  method, 
since  it  would  make  the  action  of  the  machine 
dependent  on  some  other  source  of  electric 
supply.  It  is  possible  to  dispense  with  this 
extraneous  original  source  of  exciting  current 
by  letting  the  machine  excite  itself.  Imagine 
the  current  coming  out  of  the  brush  marked 
positive  in  Fig.  17  not  led  straight  away  into 
the  external  circuit,  but  passed  first  through 
the  magnetising  coils  of  the  field  system. 


DYNAMIC'  GENERATION         199 

Before  the  current  flows  there  is  no  magnetism 
in  this  system,  or,  to  speak  more  correctly, 
there  is  but  a  very  feeble  magnetisation.  It 
is  next  to  impossible  to  have  any  piece  of 
iron  absolutely  devoid  of  any  trace  of  magnet- 
ism. The  very  act  of  machining  the  iron 
during  the  process  of  manufacture  is  sufficient 
to  produce  some  feeble  magnetisation.  This 
fact  the  reader  may  test  for  himself  in  a  very 
simple  manner.  Let  him  take  an  ordinary 
kitchen  poker,  hold  it  north- south  and  twist 
it  with  his  hands.  If  he  then  approaches  one 
end  to  a  compass  needle  and  then  the  other, 
he  will  find  that  the  poker  has  become  a 
feeble  magnet.  By  reversing  the  position 
and  twisting  again  he  will  be  able  to  reverse 
the  polarity,  thus  proving  that  it  is  the  feeble 
influence  of  the  earth's  magnetism  which, 
combined  with  the  mechanical  stress  on 
the  molecules  due  to  the  twisting,  has  pro- 
duced the  magnetisation.  The  material  of 
the  field-magnet  undergoes  during  the  process 
of  being  worked  into  shape  a  good  deal  of 
mechanical  stressing,  and  hence  becomes 
magnetic.  There  is  thus,  to  start  with,  some 
feeble  magnetisation  in  the  system.  The 
corresponding  e.m.f.  produced  at  the  brushes 
is  also  correspondingly  feeble,  but  if  the 


200  ELECTRICITY 

current  is  led  round  the  exciting  coils  in  the 
proper  sense,  this  feeble  current  will  slightly 
increase  the  original  magnetisation,  this  in 
turn  will  produce  a  slightly  greater  e.m.f., 
this  again  will  strengthen  the  field,  and  so  on 
until  the  machine  is  fully  excited.  We  have 
here  the  principle  of  "  self-excitation."  Once 
the  machine  has  been  excited  there  remains 
what  may  be  called  "  residual  magnetism," 
and  the  process  of  self-exciting  takes  place 
more  readily.  A  machine  in  which  the  whole 
of  the  armature  current  is  led  round  the 
exciting  coils  is  called  a  "  series  machine," 
which  term  is  chosen  to  indicate,  that  the 
exciting  coils  are  coupled  in  series  with 
the  external  circuit.  Since  the  whole  of  the 
current  is  used  for  excitation  a  moderate 
number  of  turns  in  the  series  coils  suffices. 
But  these  must  be  of  sufficiently  stout  wire  to 
carry  the  whole  of  the  current. 

Now  let  us  wind  these  coils  with  much 
finer  wire,  but,  to  make  up  for  the  lesser 
current  which  such  wire  can  take,  let  us  use 
a  much  larger  number  of  turns.  The  current 
which  we  wish  to  have  in  the  external  circuit 
is  much  too  large  to  be  carried  by  this  fine 
wire  coil,  and  we  must  therefore  feed  it 
directly  from  the  brushes.  The  exciting  coil 


DYNAMIC  GENERATION         201 

forms  an  electrical  shunt  to  the  external 
circuit,  and  machines  of  this  kind  are  there- 
fore called  "  shunt  machines." 

Some  of  the  e.m.f .  induced  in  the  armature 
is  necessarily  lost  in  overcoming  the  internal 
resistance  of  the  machine,  so  that  the  e.m.f. 
available  at  the  terminals  is  a  little  smaller 
than  the  induced  e.m.f.,  the  difference  being 
the  greater,  the  greater  is  the  current  the 
machine  is  called  upon  to  furnish.  Since  the 
excitation  of  a  shunt  machine  is  proportional 
to  the  potential  difference  at  its  brushes,  and 
since  this  decreases  with  the  external  current, 
such  a  machine  cannot  give  an  absolutely 
constant  voltage.  Its  voltage  will  slightly 
drop  with  an  increase  of  external  current. 
On  the  other  hand,  a  series  machine  is  excited 
by  the  external  current,  and  if  this  increases 
the  excitation  also  increases,  so  that  within 
certain  limits  the  voltage  rises  with  the 
external  current.  We  have  thus  in  the  two 
types  contradictory  working  conditions.  If 
the  machine  is  "  series  excited,"  the  terminal 
e.m.f.  rises  with  an  increase  of  load;  if  it  is 
"  shunt  excited "  the  terminal  e.m.f.  drops 
with  an  increase  of  load.  If  then  we  combine 
these  two  methods  of  excitation,  that  is,  if 
we  magnetise  the  field  system  both  by  a  shunt 


202  ELECTRICITY 

and  a  series  winding,  we  can  so  proportion 
these  coils  that  the  terminal  voltage  shall 
remain  sensibly  the  same  over  a  large  range 
of  external  load.  Machines  of  this  kind  are 
called  "  compound  machines." 

Any  dynamo  may  be  used  as  an  electric 
motor.  The  type  most  generally  used  is  the 
shunt  machine,  since  its  speed,  even  under 
large  variations  of  mechanical  load,  remains 
fairly  constant. 


CHAPTER  VIII 

ALTERNATING   CURRENTS 

WHEN  we  speak  of  a  current  flowing  along 
a  wire,  we  conceive  this  process  as  the  transfer 
of  a  something  called  electricity  from  one 
end  of  the  wire  to  the  other.  If  by  some 
means  the  potential  of  the  near  end  of  the  wire 
can  be  kept  higher  than  that  at  the  far  end, 
the  direction  of  flow  will  be  outwards ;  in  the 
opposite  case  (near  end  at  a  lower  potential 
than  far  end),  it  will  be  inwards.  This  mental 
picture  of  an  electric  current*  is  obviously 
incomplete.  To  say  that  the  near,  or  home 
end  of  a  wire  is  raised  to  a  higher  potential 
than  the  far  end,  is  the  same  thing  as  to  say 
that  we  discharge  positive  electricity,  say  from 
a  voltaic  cell,  into  the  home  end ;  but  we  have 
seen  that  whenever  a  certain  quantity  of 
positive  electricity  is  generated,  an  equal 
quantity  of  negative  electricity  is  also  gener- 
ated. Unless  this  can  flow  away  no  positive 
electricity  can  flow  into  the  home  end  of  the 
203 


204  ELECTRICITY 

wire.  Thus  we  see  that  we  must  have  a 
second  wire  connected  to  the  negative  pole 
at  the  home  end,  and  to  the  first  wire  at 
the  far  end.  With  one  wire  alone  we  can- 
not transmit  electricity  from  one  point  in 
space  to  another.  We  must  always  have  two 
wires,  one  outgoing,  the  other  returning. 
We  must,  in  fact,  always  have  a  closed  loop. 
The  loop  may  be  quite  narrow  and  many  miles 
long,  but  it  must  be  a  closed  circuit.  Since 
the  object  of  sending  electricity  over  a  certain 
distance  is  not  to  merely  cause  a  current  to 
flow  in  the  two  wires,  but  to  do  some  useful 
work  at  the  far  end,  we  must  not  join  the  two 
wires  at  the  far  end  directly,  but  must  make 
the  connection  by  way  of  some  apparatus  in 
which  the  electric  current  is  to  be  utilised. 
At  one  end  of  our  electric  line  consisting  of 
two  wires  we  have  the  apparatus  which 
generates  electricity,  at  the  other,  we  have  the 
apparatus  which  utilises  it. 

Let  the  generator  at  the  home  end  be 
a  dynamo,  and  the  apparatus  at  the  far 
end  a  lamp.  Since  the  current  in  the  out- 
going wire  is  always  exactly  of  the  same 
strength  as  that  in  the  incoming  wire,  there 
is  no  accumulation  of  electricity  in  the 
lamp;  there  is  only  a  conversion  of  the 


ALTERNATING   CURRENTS       205 

energy  represented  by  the  product  of  current 
and  drop  of  e.m.f.  on  passing  the  lamp  into 
heat  energy,  some  of  which  appears  as  light 
waves.  As  far  as  this  conversion  is  concerned, 
the  direction  in  which  the  current  flows  is 
quite  immaterial.  If  the  current  always  flows 
the  same  way,  we  call  it  a  continuous  or  'direct 
current  (abbreviation  D.C.).  If  the  current 
changes  its  direction  periodically,  we  call  it 
an  alternating  current  (abbreviation  A.C.). 

When  a  current  changes  its  direction  or 
sense  of  flow,  there  must  necessarily  be  a 
moment  when  the  flow  is  neither  in  one  nor  in 
the  other  direction;  in  other  words,  for  a 
moment  there  is  no  current  at  all.  We  say 
the  current  strength  passes  from  a  positive 
value  through  zero  to  a  negative  value. 
Alternating  currents  are  produced  by  machines 
of  the  type  shown  in  Fig.  15.  As  the  poles 
sweep  by  the  active  wires  the  induced  e.m.f., 
and  therefore  also  the  resultant  current, 
changes  gradually,  and  if  we  represent  this 
change  graphically  by  plotting  time  on  the 
horizontal  and  either  e.m.f.  or  current  on  the 
vertical,  we  get  a  wavy  line  as  shown  in  Fig. 
19.  The  distance  a  to  b  is  called  the  periodic 
time  of  the  current,  and  the  greatest  amplitude 
of  the  wave  is  called  the  "  crest  value  "  of  the 


206 


ELECTRICITY 


current.  A  complete  wave  from  a  to  b  is 
called  a  "  cycle  "  or  "  period,"  and  the  number 
of  cycles  occurring  in  a  second  is  called  the 
"  periodicity  "  or  "  frequency  "  of  the  current. 
In  most  electricity  works  supplying  current 
for  lighting  the  frequency  is  50 ;  if  the  supply 
is  mainly  for  motive  power  the  frequency  is 
lower,  generally  25,  and  for  electric  railways  a 


6/ 


FIG.  19. 

still  lower  standard  is  likely  to  be  generally 
accepted. 

It  will  be  obvious  that,  in  electric  working 
of  main  lines  of  railways,  some  agreement 
between  the  different  countries  as  to  a 
standard  frequency  is  highly  desirable,  for  a 
change  of  engine  when  passing  a  frontier  would 
be  a  useless  complication  in  the  service.  A 
beginning  in  the  direction  of  internation- 
ally standardising  the  frequency  for  electric 


ALTERNATING  CURRENTS      207 

railways  has  already  been  made  by  Prussia, 
Baden  and  Bavaria,  who  have  agreed  on  16|. 
This  figure  has  been  arrived  at  by  the  con- 
sideration that  in  many  cases  the  possibility 
of  interchanging  power  between  a  railway 
and  general  supply  might  be  convenient. 
Machinery  for  converting  frequency  can  be 
built  and  worked  most  economically  if  the 
ratio  of  conversion  is  given  by  whole  numbers, 
such  as  1  to  2  or  1  to  3.  Since  general  supply 
systems  are  mostly  working  with  a  frequency 
of  50,  and  the  conversion  to  half  that  frequency 
would  still  leave  the  frequency  a  little  too  high 
for  the  attainment  of  best  working  conditions 
in  railway  propulsion,  a  converting  ratio  of 
1  to  3  has  been  adopted  by  the  States  above- 
mentioned.  This  gives  for  the  railway  a 
frequency  of  16f.  Italy  and  Switzerland 
have  adopted  a  standard  of  15,  but  with  a 
latitude  of  10  per  cent,  up  or  down,  so  that  at 
the  higher  figure  they  come  very  nearly  into 
line  with  the  German  standard,  whilst  at  the 
lower  figure  the  Swiss  railways  have  the 
possibility  of  linking  up,  by  means  of  frequency 
transformers,  with  some  existing  works  for 
general  supply,  whose  frequency  is  in  some 
cases  as  low  as  42. 

Whatever  may  be  the  frequency  adopted 


208  ELECTRICITY 

in  any  particular  case,  it  will  be  obvious  that 
the  power  of  an  A.C.  must  depend  on  its  e.m.f* 
and  strength.  But  how  shall  we  define  either, 
since  both  are  continuously  varying  ?  Shall 
we,  in  defining  the  strength  of  an  A.C.,  give 
its  crest  value  as  so  many  amperes,  or  shall 
we  give  some  smaller  value  ?  Apparently 
the  simplest  plan  would  be  to  give  the  crest 
value,  but  this  would  not  be  a  true  measure. 
If  we  take  by  way  of  illustration  the  case  of.  a 
lamp  lighted  by  passing  an  A.C.  through  the 
filament,  we  have  seen  that  twice  during  each 
cycle  there  is  a  moment  when  the  current  is 
zero.  At  those  times  the  lamp  receives  no 
power,  whilst  at  the  times  when  the  current 
has  crest  value  it  receives  a  maximum  of 
power.  The  average  power  absorbed  by  the 
lamp  must  therefore  be  something  between 
this  maximum  power  and  zero.  If,  then,  we 
define  the  strength  of  the  current  by  stating 
its  crest  value,  we  overestimate  it.  The 
proper  basis  for  estimating  the  strength  of 
an  A.C.  is  obviously  that  of  equal  effect 
produced  by  a  B.C.,  and  we  may  thus  speak 
of  the  "  effective  "  (sometimes  also  called  the 
"  virtual ")  value  of  an  A.C.  With  modern  A.C. 
machines  the  shape  of  the  e.m.f.  and  current 
curve  shown  in  Fig.  19  closely  approaches  a 


ALTERNATING  CURRENTS      209 

sine  curve.  To  draw  such  a  curve  we  may 
proceed  as  follows :  Draw,  as  shown  in  Fig. 
20,  a  circle  with  a  radius  equal  to  the  crest 
value  of  the  current  in  any  convenient  scale. 
Divide  out  the  circle  into  a  number  of  equal 
parts,  and  divide  the  line  a  b  in  Fig.  19  into 
the  same  number  of  equal  parts.  Now  let  the 
radius  rotate,  and  every  time  it  comes  to  one  of 


FIG.  20. 

the  points  marked  out  on  the  circle,  measure 
the  height  of  this  point  over  the  horizontal, 
and  plot  this  height  over  the  horizontal  in 
Fig.  19  at  the  corresponding  division  point. 
By  the  time  we  have  once  gone  round  the  circle, 
we  shall  have  obtained,  in  Fig.  19,  all  the  points 
of  the  sine  curve  between  a  and  b  which  are 
required  to  draw  this  curve.  The  rotating 
radius  is  called  a  "  vector,"  in  this  case  a 
"  current  vector,"  since  its  projection  on  a 
vertical  line  gives  at  any  moment  during  its 


210  ELECTRICITY 

revolution  the  instantaneous  value  of  the 
current.  Thus  the  value  of  the  A.C.  cor- 
responding to  the  vector  position  A  is  AB. 
The  instantaneous  value  of  the  power  at  that 
moment  is  the  product  of  the  current  AB  into 
the  e.m.f.  over  the  lamp  terminals  at  that 
moment.  Now  this  e.m.f.  is,  by  Ohm's  law, 
the  product  of  current  and  resistance,  so  that 
the  instantaneous  power  is  proportional  to  the 
square  of  the  length  AB.  If,  then,  we  wish  to 
ascertain  what  will  be  the  average  power 
during  a  complete  cycle,  we  would  have  to 
draw  the  vector  in  all  the  positions  given 
by  the  marked-out  points  on  the  circle, 
square  all  the  lengths,  add  the  squares  up, 
and  divide  by  the  number  of  positions 
to  which  we  have  applied  this  arith- 
metical process.  Taking  the  square  root 
of  this  figure  gives  a  length,  and  measuring 
this  length  with  the  ampere  scale  which  we 
originally  used  in  determining  the  length  of  the 
vector  current,  we  get  the  effective  current.  To 
actually  carry  out  such  a  calculation  would  be 
very  laborious;  fortunately  we  can  avoid 
this  mathematical  drudgery  by  making  use 
of  the  well-known  Pythagorean  axiom  that  the 
sum  of  the  squares  of  the  kathetes  in  a  rect- 
angular triangle  is  equal  to  the  square  of  the 


ALTERNATING  CURRENTS      211 

hypotenuse.  Let  us  assume  that  instead  of 
making  the  calculation  for  one  vector  only,  we 
make  it  simultaneously  for  two,  such  as  A 
and  A15  situate  at  right  angles  to  each  other. 
Since  we  count  each  vector  twice  over,  the 
result  will  also  be  twice  the  true  value.  We 
have  now  to  form  the  sum  of  AB2  and  AjB2, 
but  by  the  axiom  just  mentioned,  this  is  always 
equal  to  the  square  of  the  vector  itself.  Since 
this  is  the  same  for  all  positions,  the  mean  is 
the  same  as  each  part,  but  since  we  counted 
each  vector  twice,  the  mean  is  twice  the  real 
value.  The  square  of  the  effective  value  of 
the  current  is  therefore  one-half  of  the  square 
of  the  crest  value,  or  the  effective  value  is 
found  by  dividing  the  crest  value  by  the  square 
root  of  2.  This  is  1*4,  and  1  divided  by  1*4 
is  0*71.  We  thus  find  that  the  effective  value 
of  an  A.C.  is  71  per  cent,  of  its  crest  value.  The 
same  relation  applies  of  course  also  to  the 
e.m.f .  The  same  reasoning  which  has  here  been 
applied  when  discussing  the  passage  of  the  A.C. 
through  the  lamp.,  also  applies  to  its  passage 
through  any  measuring  instrument  adapted 
for  A.C.  Amperemeters  and  voltmeters 
give  the  effective  values,  not  the  crest  values. 
In  the  case  of  an  incandescent  lamp,  the 
product  of  the  current  shown  on  such  an 


212  ELECTRICITY 

amperemeter,  with  the  e.m.f .  shown  on  such  a 
voltmeter,  gives  the  true  power  absorbed  by 
the  lamp. 

If  the  receiving  apparatus  is  an  electric 
motor  this  simple  relation  does  not  necessarily 
hold  good.  The  product  of  current  and 
pressure  may  be  the  true  power,  but  it  is 
not  necessarily  the  true  power.  It  will  give 
the  true  power  if  the  crest  values  of  current 
and  pressure  occur  at  the  same  moment,  but 
if  there  is  a  time  displacement  between  their 
occurrence,  then  the  true  power  is  smaller 
than  the  product  of  current  and  pressure. 
Now  why  should  there  be  a  time  displace- 
ment ?  The  reason  is  this.  In  a  motor  there 
are  coils  of  wire  embedded  in  iron  and  the 
current  has  to  pass  through  these  coils.  The 
current  produces  thus  a  flux  of  magnetic 
lines  which  grow  and  diminish  and  reverse 
their  direction  with  the  corresponding  changes 
in  the  current  strength.  A  coil  interlinked 
with  a  changing  magnetic  flux  becomes,  as  was 
shown,  the  seat  of  an  e.m.f.  When  the  current 
passes  through  its  crest  value  the  rate  of 
change,  and  therefore  the  e.m.f.,  is  zero; 
when  the  current  passes  through  zero  value 
its  rate  of  change  is  a  maximum,  and  at  those 
times  the  self -induced  e.m.f.  is  also  a  maximum. 


ALTERNATING  CURRENTS       213 

We  thus  find  that  in  point  of  time  the  e.m.f . 
induced  by  the  current  in  its  own  circuit  does 
not  coincide  with  the  current,  but  lags  by 
a  quarter  of  a  period  behind  the  current. 
The  e.m.f.  impressed  on  the  motor  must 
therefore  not  only  have  a  component  which 
is  co-phasal  with  the  current  and  which  gives 
the  power,  but  also  a  component  equal  and 


FIG.  21. 

opposite  to  that  which  the  current  induces 
itself,  and  which  therefore  in  point  of  time 
must  lead  over  the  current.  The  vector  of 
the  impressed  e.m.f.  and  of  the  resulting 
current  are  no  longer  co-phasal,  but  form  an 
angle  (p  as  shown  in  Fig.  21,  where  OE  re- 
presents the  e.m.f.  vector  and  OI  the  current 
vector.  The  component  of  OE  in  the  direc- 
tion of  the  current  is  OE  cos  <p,  and  the  true 
power  is  therefore 

P  =  ei  cos  <p 


214  ELECTRICITY 

Cos  <p  is  called  the  power  factor,  and  it  is 
the  aim  of  the  designer  to  so  arrange  the 
circuits  of  a  machine  as  to  make  the  power 
factor  as  near  unity  as  possible.  A  low 
power  .  factor  is  objectionable  because  an 
unduly  large  current  or  an  unduly  large 
voltage  is  required  to  produce  a  given  amount 
of  power.  This  means  greater  bulk  and  cost 
of  machinery,  and  also  stouter  cables  for  the 
transmission  of  the  current  from  the  generating 
station  to  the  places  of  consumption.  The 
average  power  factor  of  electricity  works 
supplying  alternating  currents  is  0-8  or  even 
less.  This  is  due  to  the  supply  of  current 
to  electric  motors  and  arc  lamps.  Small 
motors  may  have  a  power  factor  as  low  as 
60  per  cent.,  large  motors  may  have  a  power 
factor  as  high  as  90  per  cent.,  and  with  some 
special  types  even  unity  may  be  reached, 
but  as  the  bulk  of  the  supply  is  taken  in 
small  and  moderate-sized  motors,  an  average 
of  0-8  is  as  high  as  can  reasonably  be  expected. 

The  current  delivered  at  the  places  of 
consumption  is  very  seldom  used  at  the 
pressure  of  delivery.  This  is  generally  far 
too  high  for  the  lamps  or  motors  employed. 
The  possibility  of  using  high  and  extremely 
high  pressure  is  one  of  the  advantages  of 


ALTERNATING   CURRENTS       215 

A.C.  as  far  as  the  conveyance  of  electric  power 
to  great  distances  is  concerned,  because  the 
higher  the  pressure  the  smaller  the  current 
strength  corresponding  to  a  given  amount 
of  power,  and  the  smaller  the  quantity  of 
metal  required  in  the  transmission  line.  But 
if  high  pressure  is  an  economic  necessity  as 
regards  transmission  of  power,  it  is  an  ob- 
jection as  regards  the  utilisation  of  power. 
We  must  therefore  transform  at  the  place  of 
utilisation  the  small  current  of  high  pressure 
into  a  large  current  of  low  pressure.  This  is 
done  by  an  apparatus  called  the  "  trans- 
former." The  principle,  on  which  the  trans- 
former works,  is  illustrated  in  Fig.  22.  The 
high  pressure  current  is  delivered  at  the 
terminals  Tx  Tr  To  these  is  connected  a 
coil  of  many  turns  of  wire  wound  on  an  iron 
core  C.  On  the  same  core  is  placed  a  second 
coil  of  fewer  turns  of  stouter  wire,  and  the 
consuming  devices  (lamps  or  motors)  are 
connected  to  the  terminals  T2  T2  of  this  coil. 
The  high -pressure  current  passing  through  the 
winding  of  the  primary  coil  P,  magrietises 
the  iron  core,  and  since  the  secondary  coil  C 
is  encircling  this  core  also,  it  is  traversed  by 
the  flux  of  force  produced  by  the  primary 
current.  Thus  by  electromagnetic  induction 


216 


ELECTRICITY 


an  e.m.f.  is  generated  in  the  coil  S,  and  this  is 
the  real  source  of  the  secondary  current 
supplied  to  the  consuming  devices.  Fig.  22 
is  only  a  diagrammatic  representation'  of  a 
principle,  not  of  the  actual  apparatus.  In 
reality  the  two  coils  are  placed  much  closer 
together  and  the  iron  core  has  not  open  ends, 
but  is  in  the  form  of  a  closed  magnetic  circuit. 
It  may  have  the  shape  of  a  rectangular  frame 


FIG.  22. 

built  up  of  thin  iron  plates,  the  two  longer 
limbs  of  the  rectangle  forming  the  two  cores 
on  which  the  coils  are  placed,  whilst  the 
shorter  traversing  limbs  act  as  yokes  to  com- 
plete the  magnetic  circuit.  This  type  is 
called  a  "  core  transformer."  In  another 
type  there  is  only  one  central  core,  and  the 
magnetic  circuit  is  closed  on  both  sides  by 
yokes  forming  each  three  sides  of  a  rectangle, 
and  thus  enclosing  the  coils  on  either  side 


ALTERNATING  CURRENTS      217 

with  a  kind  of  iron  shell.  This  type  is  called 
a  "  shell  transformer."  In  either  type  the 
primary  and  secondary  coils  are  placed  as 
close  together  as  is  compatible  with  an 
efficient  insulation  between  them.  This  is 
done  in  order  that  the  secondary  winding 
may  be  traversed  by  as  near  as  possible  the 
whole  flux  which  passes  through  the  primary 
winding,  and  thus  the  ratio  of  transformation 
is  very  nearly  equal  to  the  ratio  between  the 
number  of  turns  in  the  two  windings. 

The  efficiency  of  transformers  is  remarkably 
high.  Under  efficiency  must  be  understood 
the  ratio  of  the  power  received  by  the 
primary  circuit  to  the  power  given  out  by 
the  secondary  circuit.  No  machine  can  have 
an  efficiency  of  unity ;  the  output  must  always 
be  smaller  than  the  input,  but  the  difference 
in  the  case  of  a  transformer  is  much  smaller 
than  in  the  case  of  a  dynamo  of  equal  power. 
Even  a  small  transformer  of  but  a  few  KW. 
power  may  have  as  much  as  90  per  cent, 
efficiency,  whilst  large  transformers  of  1000 
KW.  may  reach  98  or  98 J  per  cent. 

Alternating  currents  are  produced  by 
machines  of  the  type  represented  by  Fig.  15. 
Such  a  machine  is  simply  an  implement  for 
converting  mechanical  power  into  the  electric 


218  ELECTRICITY 

power  represented  by  the  A.C.  flowing  under 
the  potential  difference  corresponding  to  the 
excitation  of  the  magnetic  system.  Obvi- 
ously the  converse  process  must  also  be 
possible.  If  we  supply  electric  power  in  the 
shape  of  an  A.C.  to  the  armature  of  this 
machine  and  keep  the  field-magnets  excited 
as  before,  we  must  be  able  to  obtain  mechanical 
power  from  the  shaft.  But  then  the  speed 
must  be  exactly  that  corresponding  to  the 
frequency  of  the  A.C.  supplied.  To  use  a 
machine  of  this  kind  as  an  electric  motor  we 
must  first  bring  it  up  to  speed  by  some  means, 
and  only  if  the  speed  is  exactly  such  that  the 
rhythm  of  the  passage  of  the  poles  in  front 
of  the  armature  coils  synchronises  with  the 
frequency  of  the  available  supply  may  we 
switch  this  on  to  the  armature.  Electric 
motors  of  this  kind  are  therefore  called 
"  synchronous  motors."  The  necessity  of 
bringing  the  motor  first  up  to  speed  before 
being  able  to  switch  the  driving  current  on 
is  an  inconvenience  which  renders  such 
motors  unsuitable  for  general  purposes. 

To  the  late  Professor  Ferraris  of  Turin  be- 
longs the  merit  of  having  discovered  a  principle 
of  alternating  current  working  by  which  the 
motor  may  be  started  by  the  alternating 


ALTERNATING  CURRENTS      219 

current  itself  without  bringing  it  first  up  to 
the  speed  of  synchronism.  Motors  of  this 
kind  are  called  "  asynchronous  "  or  "  non- 
synchronous  "  motors.  As  already  stated, 
Ferraris  himself  did  not  realise  the  enormous 
technical  importance  of  his  discovery,  but 


FIG.  23. 

this  does  not  detract  from  the  merit  of  having 
made  it.  The  classical  experiment  of  Ferraris 
is  illustrated  in  Fig.  23.  A  copper  cylinder 
C  is  suspended  within  two  coils  A  and  B  so 
placed  that  their  planes  stand  at  right  angles 
to  each  other.  For  the  sake  of  clearness  the 
illustration  shows  coils  of  only  one  turn  each, 
in  reality  each  coil  contains  a  large  number 


220  ELECTRICITY 

of  turns.  Now  imagine  a  machine  as  shown 
in  Fig.  15  having  two  independent  windings  as 
pointed  out  on  p.  186.  Let  one  winding 
supply  current  to  the  coil  A  and  the  other  to 
the  coil  B.  The  phases  of  the  two  currents 
are  displaced  in  point  of  time  by  a  quarter 
period.  If  the  current  in  A  has  crest  value 
that  in  B  is  zero  and  vice  versa.  The 
magnetic  field  produced  by  these  coils  and 
passing  through  the  copper  cylinder  will  at 
these  two  moments  have  the  direction  at 
right  angles  to  the  plane  of  coil  A  and  to 
that  of  coil  B  respectively.  At  intermediate 
times,  when  there  is  some  current  in  both 
coils,  the  magnetic  field  will  be  due  to  the 
combined  effect  of  both  currents,  and  its 
direction  will  be  intermediate  between  the 
two  positions  mentioned.  We  thus  get  a 
"  revolving  magnetic  field,"  the  number  of 
complete  revolutions  performed  in  a  second 
being  equal  to  the  frequency.  It  is  as  though 
a  physical  magnet  were  whirled  round  the 
copper  cylinder.  The  lines  of  force  of  this 
revolving  field  cut  through  the  metal  of  the 
cylinder  and  thus  create  induced  currents, 
which  in  combination  with  the  field  produced 
by  the  two  coils  exert  a  drag  on  the  surface 
of  the  cylinder  and  cause  it  to  rotate  in  the 


ALTERNATING  CURRENTS      221 

same  direction.  This  drag  is  but  a  feeble 
force,  but  it  is  easy  to  augment  it  by  a  proper 
disposition  of  the  parts.  In  the  first  place  it 
should  be  noted  that  the  lines  of  force  are 
entirely  flowing  through  air,  and  consequently 
the  induction  is  weak.  If  we  were  to  provide  an 
iron  path  for  them,  the  induction  would  become 


FIG.  24. 

immensely  stronger.  This  is  the  direction  in 
which  Ferraris'  discovery  was  developed  by 
various  designers.  The  general  principle  of  im- 
proving the  magnetic  path  is  shown  in  Fig.  24. 
The  coils  A  and  B  are  embedded  in  an 
external  iron  cylinder,  and  thus  the  magnetic 
reluctance  of  the  external  path  of  the  lines 
of  force  is  reduced  to  a  mere  fraction  of  what 
it  was  before.  The  magnetic  reluctance  of 


222  ELECTRICITY 

the  internal  part  of  the  path  is  likewise 
reduced  considerably  by  making  the  internal 
cylinder  not  entirely  of  copper,  but  using  an 
iron  cylinder  with  a  mere  coating  of  copper. 
Thus  there  is  only  the  narrow  space  left 
between  the  two  cylinders  where  the  lines  of 
force  have  to  be  forced  across  a  non-magnetic 
medium,  and  the  result  is  a  very  large  increase 
in  the  total  magnetic  flux.  At  the  moment 
that  the  current  in  coil  A  has  crest  value  the 
flux  has  the  direction  as  indicated  by  the 
arrow  1.  A  moment  later,  when  B  also 
becomes  active,  the  direction  of  the  flux  is 
shown  by  the  arrow  2.  A  quarter  period  later 
when  the  current  in  A  is  zero  and  that  in  B 
has  crest  value,  the  flux  is  due  to  B  only  and  has 
the  direction  3.  A  little  later  still  the  current 
in  B  has  diminished  and  that  in  A  has  grown  to 
some  negative  value.  Thus  the  flux  is  turned 
into  the  position  4  and  so  on,  the  flux  gradually 
passing  through  the  directions  given  by  the 
arrows  5, 6, 7, 8,  and  then  the  cycle  begins  again. 
The  motor  shown  in  Fig.  24  has  still  an 
imperfection.  No  definite  path  is  provided 
for  the  current  induced  in  the  revolving 
cylinder,  technically  termed  the  "  rotor." 
The  currents  flow  more  or  less  irregularly 
within  the  whole  mass  of  the  metal,  and  some 


ALTERNATING  CURRENTS      223 

of  them  are  therefore  not  in  the  most  advan- 
tageous position  for  exerting  mechanical  force. 
The  improvement  necessary  to  overcome  this 
imperfection  is  obvious.  If  we  replace  the 
copper  cylinder  forming  a  coating  to  the  iron 
core  by  a  regular  copper  winding  embedded 
in  the  surface  of  this  core,  we  constrain  the 
currents  to  flow  along  definite  paths,  which 
relatively  to  the  currents  in  the  fixed  part  or 
"  stator  "  are  always  in  the  most  efficient 
position  for  the  production  of  mechanical 
force.  The  modern  non-synchronous  motor 
is  therefore  provided  with  a  winding  both  on 
the  stator  and  on  the  rotor;  and  both  wind- 
ings are  embedded  in  slots,  so  that  the  reluct- 
ance of  the  magnetic  circuit  is  mainly  that  of 
the  air-gap  between  the  outer  surface  of  the 
rotor  and  the  inner  surface  of  the  stator. 
This  need  not  be  larger  than  a  mere  mechanical 
clearance  allowing  the  inner  part  to  revolve 
without  touching. 

A  lesser  imperfection  of  the  motor  shown  in 
Fig.  24  is  due  to  the  employment  of  only  two 
currents.  The  result  of  this  arrangement  is 
that  the  strength  of  the  revolving  field  is 
subject  to  certain  fluctuations.  At  the  mo- 
ment that  the  current  in  A  has  crest  value  the 
maximum  value  of  the  induction  in  the  air-gap 


224  ELECTRICITY 

is  somewhat  less  than  one-eighth  of  a  period 
later  when  both  coils  are  active.  The  field 
thus  is  not  only  rotating,  but  also  to  a  slight 
extent  pulsating,  and  these  pulsations  give 
rise  to  parasitic  currents  which  contribute 
nothing  to  the  driving  force  and  only  waste 
power.  By  certain  methods  of  grouping  the 
wires  it  is  possible  to  reduce  these  pulsations 
to  a  tolerable  amount,  but  a  better  way  still 
is  to  build  the  motor  for  three-phase  current. 
The  combined  action  of  three  currents  mutu- 
ally one -third  of  a  period  apart  in  point  of 
time  results  in  the  production  of  a  sensibly 
constant  flux  revolving  at  constant  speed.  A 
mechanical  analogy  of  the  kind  of  irregularity 
to  be  expected  in  the  cases  of  two-phase  and 
three-phase  motors  is  furnished  by  deep  well 
pumps.  With  such  pumps  it  is  important 
that  the  rate  of  flow  of  water  in  the  delivery 
pipe  shall  be  as  uniform  as  possible,  because 
with  a  great  length  of  delivery  pipe  the 
column  of  water,  alternately  accelerated  and 
retarded  if  the  flow  is  not  uniform,  throws  con- 
siderable stresses  on  the  machinery.  A  pump 
with  one  cylinder  only  is,  therefore,  even 
if  a  large  air-vessel  is  used  as  equaliser, 
not  so  satisfactory  as  a  pump  with  two 
cylinders  and  cranks  set  at  90  degrees.  More 


ALTERNATING  CURRENTS      225 

satisfactory  still  is  a  pump  with  three  cylinders 
and  cranks  set  120  degrees  apart.  With  this 
arrangement  the  flow  of  water  is  so  uniform 
that  the  use  of  an  air-vessel  as  an  equalising 
agent  becomes  almost  superfluous.  The  two- 
cylinder  pump  is  the  mechanical  analogy  to 
the  two-phase  motor,  and  the  three-cylinder 
pump  is  that  of  the  three-phase  motor. 

Since,  as  will  be  shown  in  the  next  chapter, 
the  use  of  three  phases  has  also  the  advantage 
of  considerable  economy  in  the  amount  of 
metal  required  to  carry  a  given  power  over  a 
given  distance,  the  use  of  three-phase  current 
for  motive  power  purposes  has  become  almost 
universal. 

Small  asynchronous  motors  are  sometimes 
made  with  what  is  technically  known  as  a 
"  squirrel  cage  rotor,"  the  name  being  derived 
from  the  peculiar  type  of  winding  used.  In 
the  ordinary  sense  of  the  word  the  conductors 
on  the  rotor  do  not  form  a  winding  of  wire, 
but  a  series  of  copper  bars  laid  along  and 
embedded  into  the  surface  of  the  core.  At 
either  end  the  bars  are  all  joined  up  by  metal 
rings,  thus  forming  a  kind  of  squirrel  cage. 
This  construction  has  the  advantage  of  great 
mechanical  simplicity  and  strength,  but  the 

disadvantage  that  at  starting  the  motor  takes 
p 


226  ELECTRICITY 

a  large  current  at  a  low  power  factor.  At 
starting  the  rotor  is  at  rest  and  only  gradually 
gathers  speed.  Whilst  running  slowly  the 
frequency  with  which  the  rotor  bars  are  cut 
by  the  revolving  field  is  great,  and  conse- 
quently the  e.m.f.  and  the  rotor  current  are 
also  great.  A  great  rotor  current  means  a 
weakening  of  the  flux  originally  produced  by 
the  stator  current,  but  as  this  flux  is  mainly 
instrumental  in  balancing  the  e.m.f.  impressed 
on  the  stator  terminals,  and  since  this  e.m.f. 
is  constant,  no  appreciable  weakening  can 
take  place.  The  action  of  the  machine  is 
that  it  automatically  admits  more  current 
through  the  stator  to  make  up  for  the  weaken- 
ing effect  produced  by  the  excessive  rotor 
current  at  starting.  A  sudden  rush  of  current 
taken  from  the  supply  terminals  is  disturbing 
to  the  rest  of  the  machinery  supplied  from 
the  same  system,  and  hence  the  use  of  squirrel- 
cage  motors  must  in  the  interest  of  all  con- 
sumers be  restricted  to  small  types.  When 
motors  of  large  power  are  required  it  is  neces- 
sary to  limit  the  excessive  rush  of  current  at 
starting,  and  this  is  done  by  using  a  rotor  with 
proper  winding,  the  terminals  of  which  are 
connected  to  slip-rings  on  the  shaft.  On 
these  slip-rings  are  placed  brushes  which  are 


ALTERNATING  CURRENTS       227 

connected  with  a  starting  resistance.  As  the 
motor  gathers  speed  this  resistance  is  gradually 
short-circuited.  Thus  at  no  time  is  there  any 
excessive  rush  of  current  in  the  primary  or 
stator  winding.  When  the  motor  has  attained 
full  speed  the  whole  of  the  starting  resistance 
is  cut  out  and  the  slip-rings  are  short-circuited. 
In  this  condition  the  speed  at  which  the  rotor 
winding  is  cut  by  the  revolving  field  is  only 
a  few  per  cent,  of  the  speed  at  starting.  It 
is  the  difference  between  the  speed  of  the 
revolving  field  and  the  speed  of  the  rotor. 
This  is  technically  termed  the  "  slip  "  of  the 
motor,  and  varies  from  about  6  per  cent,  in 
small  motors  to  2  per  cent,  in  large  motors. 
The  heavier  the  mechanical  load  on  the  motor, 
the  greater  is  the  slip.  A  motor  of  50  H.P. 
would  have  about  1 J  per  cent,  slip  at  half  load 
and  about  3  per  cent,  at  full  load,  so  that 
practically,  although  it  is  non-synchronous, 
the  speed  may  be  considered  as  approximately 
constant.  This  constancy  of  speed  under 
variable  load  is  a  desirable  feature  in  most  of  the 
industrial  uses  of  motive  power,  and  together 
with  the  great  simplicity  of  mechanical  con- 
struction explains  why  these  motors,  originally 
grown  out  of  a  scientific  discovery  made  by  a 
professor  of  physics,  have  become  so  popular. 


CHAPTER  IX 

THE   DISTRIBUTION   OF   ELECTRICITY 

As  a  mere  theoretical  proposition,  the 
transfer  of  electric  power  from  the  battery  or 
machine  in  which  it  is  generated  to  the  lamp 
or  other  apparatus  in  which  it  is  to  be  utilised 
is  quite  a  simple  affair.  A  few  wires  insulated 
from  earth  and  from  each  other  and  a  switch 
is  all  that  is  required.  But  if  we  come  to  the 
practical  proposition  of  distributing  electricity 
for  general  use,  this  seemingly  so  simple 
problem  assumes  a  very  formidable  aspect. 
The  connecting  wires  become  heavy  con- 
ductors many  miles  long,  they  may  have 
hundreds  of  ramifications  to  reach  as  many 
users  of  electricity,  the  efficient  insulation  of 
the  electric  mains  with  all  their  branches  re- 
quires special  care,  and  the  switches  may 
become  so  large  that  they  cannot  any  longer 
be  worked  by  hand,  but  require  special 
electric  motors  to  close  or  open  them.  There 
is  further  the  necessity,  on  the  one  hand,  of 
228 


DISTRIBUTION  OF  ELECTRICITY    220 

protecting  the  user  and  the  public  from 
accidental  contact  with  any  charged  con- 
ductor, and  on  the  other  the  necessity  of 
protecting  the  distributing  plant  itself  from 
injury  by  external  forces,  including  atmo- 
spheric electricity.  Thus  it  comes  that  in 
modern  works  for  the  generation  and  dis- 
tribution of  electricity  the  distributing  plant 
is  an  important  item  financially,  its  cost 
ranging  from  about  a  quarter  to  one-half  of 
the  total  capital  outlay. 

The  supply  of  electricity  in  urban  areas 
must  necessarily  be  by  means  of  cables  laid 
underground,  and  the  cost  of  these  cables  is 
one  of  the  principal  items  in  the  cost  of  the 
distributing  plant.  The  higher  the  pressure 
at  which  the  current  is  conveyed  the  smaller 
may  be  the  cross  section  of  the  cable,  but 
where  the  supply  is  for  general  purposes, 
including  domestic  lighting,  there  is  a  limit 
to  the  pressure.  Incandescent  lamps  of 
moderate  candle-power  cannot  be  made  for 
a  higher  pressure  than  250  volts,  and  even 
this  is  exceptional.  The  general  voltage  is 
220,  so  that  a  supply  to  be  generally  used 
must  be  given  at  about  that  pressure. 

The  current  in  passing  from  the  place  of 
generation  to  the  place  of  use  has  to  pass 


230  ELECTRICITY 


along  wires,  and  part  of  the  voltage  is  lost 
in  overcoming  the  ohmic  resistance  of  these 
wires.  This  loss  of  pressure  varies  directly 
with  the  current.  At  the  time  that  the 
greatest  number  of  lamps  in  any  particular 
district  are  switched  on,  the  loss  of  pressure 
in  the  cables  supplying  that  district  is  greatest, 
and  in  order  that  the  lamps  may  still  burn 
with  normal  brightness,  the  pressure  at  the 
home  end  of  the  distributing  system  must  be 
raised  to  a  value  just  sufficient  to  make  up 
for  the  loss  of  pressure  due  to  ohmic  re- 
sistance. But  an  exact  adjustment  is  im- 
possible; some  lamps  are  nearer  and  some 
farther  away  from  the  home  end  of  the  cable. 
The  current  when  it  reaches  the  nearer  lamps 
has  not  lost  quite  as  much  of  its  voltage  as 
when  it  reaches  the  farther  lamps.  To  make 
the  delivery  voltage  absolutely  right  for  every 
lamp  is  obviously  impossible,  but  we  can 
approach  this  ideal  condition  by  the  adoption 
of  the  following  principles  :  First  use  cables 
stout  enough  so  as  to  limit  the  total  loss  of 
pressure  to  a  moderate  amount,  say  10  to 
15  per  cent,  of  the  lamp  voltage;  secondly, 
divide  the  distributing  plant  into  two  distinct 
portions,  namely  "feeders"  and  "mains." 
To  explain  what  is  meant  by  these  terms, 


DISTRIBUTION  OF  ELECTRICITY    231 

and  why  by  the  adoption  of  a  particular 
method  of  using  the  conductors  a  satisfactory 
service  to  all  customers  of  an  electricity 
works  can  be  given,  let  us  take  by  way  of 
example  the  service  of  electricity  to  the  house- 
holders along  a  street  a  mile  long,  the  elec- 
tricity works  being  at  one  end  of  this  street. 
Here  we  have  some  customers  quite  close 
to  the  place  of  generation  and  others  a  mile 
away.  If  we  were  simply  to  connect  the 
home  end  of  these  cables  with  the  machines 
and  supply  the  whole  of  the  street  from  this 
one  end  only,  we  should  get  so  great  a  varia- 
tion in  the  voltage  in  different  houses  as  to 
make  the  supply  very  unsatisfactory.  The 
customers  close  by  would  get  far  too  high  a 
voltage  and  their  lamps  would  be  destroyed 
by  "  over-running,"  and  the  customers  at  the 
other  end  of  the  street  would  get  hardly  any 
light.  The  variation  of  delivery  voltage 
legally  permitted  to  public  supply  companies 
by  the  Board  of  Trade  regulations  is  plus 
or  minus  4  per  cent.,  but  even  this  seemingly 
moderate  variation  would  be  intolerable  to 
the  user  of  electric  light  if  it  occurred  suddenly. 
The  light  given  by  an  incandescent  lamp 
varies  at  a  much  greater  ratio  than  the 
voltage,  about  four  to  six  times  as  much,  so 


232  ELECTRICITY 

that  a  2  per  cent,  voltage  variation  means 
about  10  per  cent,  light  variation.  The  human 
eye  has  so  great  a  power  of  adaptation  to 
changes  in  illumination  that  a  10  per  cent, 
variation,  if  it  takes  place  very  gradually, 
will  scarcely  be  noticed,  certainly  less  than 
the  illumination  of  a  room  by  daylight  if 
clouds  are  passing  over  the  sun. 

If  a  current  were  fed  into  our  street  main  of 
a  mile  in  length  at  one  end  only,  the  voltage 
difference  between  the  two  ends  and  at 
different  times  would  be  very  much  greater 
than  2  or  even  the  4  per  cent,  allowed  by 
the  Board  of  Trade,  and  no  power  of  adapta- 
tion of  the  human  eye  could  make  such  a 
service  acceptable.  To  put  at  the  near  end 
lamps  of  higher  and  at  the  far  end  lamps  of 
lower  voltage  is  no  remedy.  At  the  time  of 
small  demand,  say  early  in  the  morning,  there 
will  be  very  little  difference  in  the  voltage  all 
along  the  street,  so  that  the  lamps  at  the  far 
end  would  be  over-run  and  soon  burn  out. 
At  times  of  great  general  demand,  the  so- 
called  "  peak- time,"  the  difference  in  voltage 
would  be  very  great.  By  grading  the  voltage 
of  the  lamps  according  to  distance  from  the 
central  station  we  can  only  slightly  mitigate 
the  evil,  but  certainly  not  cure  it.  The  exact 


DISTRIBUTION  OF  ELECTRICITY    233 

hour  when  the  peak  in  the  lighting  load  occurs 
depends  on  the  kind  of  premises  lighted.  In 
offices  it  is  between  five  and  six ;  in  residential 
districts  between  seven  and  eight,  because  at 
that  time  the  kitchen  premises  are  fully  lighted, 
the  bedrooms  are  used  by  people  dressing  for 
dinner,  and  at  the  same  time  the  reception- 
rooms  must  be  lighted  up.  Whatever  the 
property  lighted,  there  is  a  great  variation 
in  the  demand  for  current  at  different  times 
of  the  day,  and  the  cables  must  be  designed 
to  be  equal  to  the  maximum  demand  that 
may  occur. 

If  the  street  main  is  fed  at  the  home  end, 
the  total  current  sent  into  it  at  that  end  is 
proportional  to  its  length.  The  resistance 
is  also  proportional  to  its  length,  and  since 
the  drop  is  proportional  to  the  product  of 
current  and  resistance,  we  find  that  for  a 
given  density  of  supply  expressed  at  so  many 
amperes  per  yard  run,  the  voltage  drop  is 
proportional  to  the  square  of  the  length.  If, 
then,  instead  of  feeding  the  street  main  at 
one  end,  we  feed  it  in  the  middle  only,  we 
substitute  two  half-mile  lengths  for  the  single 
mile  and  we  quarter  the  voltage  drop.  To  do 
this  we  require  a  separate  cable,  the  so-called 
"  feeder,"  from  which  no  current  is  taken 


234,  ELECTRICITY 

on  the  way.  This  merely  serves  to  bring  the 
current  into  the  middle  of  the  main  where  the 
feeder  is  tapped  into  it.  We  can  still  go  a 
step  further  and  arrange  for  feeding  points 
closer  together,  so  as  to  reduce  still  further 
the  length  of  each  section  of  main  in  which 
the  voltage  drop  takes  place.  This  drop 
may  thus  be  made  exceedingly  small,  even 
at  peak-time,  but  then  we  must  make  such 
arrangements  as  will  result  in  a  constant 
voltage  at  all  the  feeding  points.  All  the 
mains  in  the  streets  of  a  town  are  arranged 
to  form  a  connected  network,  and  at  certain 
points  of  this  network,  preferably  those  close 
to  districts  of  great  demand,  the  network  is 
tapped  by  feeders.  Obviously  these  feeders 
are  not  of  equal  length  or  equal  resistance, 
arid  they  will  certainly  not  carry  equal 
currents  at  all  times  of  the  day.  It  becomes, 
therefore,  necessary  to  adjust  the  voltage 
impressed  on  each  feeder  or  group  of  feeders 
at  the  central  station  independently,  and  that 
is  "done  by  the  use  of  so-called  "boosting 
dynamos."  These  are  small  machines,  which 
may  be  regulated  so  as  to  raise  the  voltage 
at  the  home  end  of  each  feeder  by  just  the 
amount  necessary  for  making  up  what  at  any 
time  is  lost  by  ohmic  resistance  in  that  feeder. 


DISTRIBUTION  OF  ELECTRICITY    235 

By  using  an  interconnected  network, 
numerous  feeding  points,  boosted  feeders, 
and  generally  cables  of  ample  cross  section, 
it  is  thus  possible  to  give  a  perfectly  satis- 
factory service  with  a  lamp  voltage  of  220  V. 
There  remains,  however,  the  question  whether 
such  a  distributing  system  can  be  laid  down 
at  a  reasonable  cost  ?  In  most  cases  the 
answer  is  in  the  negative.  With  the  low 
pressure  of  220  volts  the  amount  of  copper 
required  for  feeders  and  mains  would  repre- 
sent a  prohibitive  outlay.  There  is  only  one 
way  in  which  we  can  economise  copper,  and 
that  is  by  raising  the  pressure^  Suppose 
we  could  get  lamps  which  will  work  satis- 
factorily with  double  the  pressure,  or  440 
volts,  then  for  the  same  power  we  should  only 
have  to  transmit  half  the  current.  If  we  also 
halve  the  cross  sections  of  all  cables  we  should 
have  the  same  absolute  voltage  drop  as  before, 
but  as  the  pressure  is  doubled,  this  means 
half  the  percentage  drop.  To  get  the  same 
percentage  drop  as  before  we  may  again 
halve  the  cross  section  of  all  the  cables,  that 
is  to  say,  by  doubling  the  pressure  the  whole 
system  will  only  require  one  quarter  the 
amount  of  copper  as  before.  This  brings  us 
into  the  region  of  the  commercial  possibility 


236  ELECTRICITY 

of  a  general  supply  of  electricity  to  house- 
holders. But  lamps  for  440  volts  are  not 
obtainable.  To  use  a  supply  at  440  volts 
with  the  lamps  at  present  on  the  market,  we 
should  have  to  use  two  in  series  connection, 
that  is  to  say,  always  burn  lamps  in  pairs. 
This  would  be  an  intolerable  restriction  to 
which  no  householder  would  submit.  Now 
suppose  for  a  moment  that  we  do  not  put  two 
neighbouring  lamps  in  series,  but  two  neigh- 
bouring houses.  This  means  that  a  tapping 
from  the  positive  main  only  is  taken  to  supply 
house  No.  20,  and  a  tapping  from  the  negative 
main  only  to  supply  house  No.  21,  the  circuit 
being  completed  by  a  wire  taken  from  the 
lamps  of  No.  20  to  those  of  No.  21.  If  both 
householders  were  to  agree  that  they  would  at 
all  times  burn  exactly  the  same  number  of 
lamps,  we  should  have  electrically  the  same 
condition  as  in  the  previous  case,  where  we 
arranged  the  lamps  in  one  house  in  pairs. 

This  arrangement  would,  however,  be  still 
more  intolerable  than  the  previous  one. 
Now  suppose  that  we  put  all  the  houses  of 
even  numbers  on  the  positive  main  and  all 
the  houses  of  odd  numbers  on  the  negative; 
further,  that  all  the  connecting  wires  between 
the  houses  are  replaced  by  a  third  main,  then 


DISTRIBUTION  OF  ELECTRICITY    237 

we  get  a  system  under  which  each  house 
having  an  even  number  would  be  connected 
to  the  positive  main  and  this  third  main, 
and  each  house  having  an  odd  number  would 
be  connected  between  the  negative  and  the 
third  main.  The  condition  that  there  shall 
be  the  same  number  of  lamps  in  use  on  the 
positive  and  the  negative  side  of  this  third 
main  will  be  almost  naturally  fulfilled,  and 
there  will  be  no  need  of  asking  householders 
to  agree  with  their  neighbours  as  to  the  number 
of  lamps  each  shall  burn  at  any  given  hour. 
With  a  sufficiently  large  number  of  houses 
connected  to  this  three -wire  main  there  will, 
by  the  law  of  averages,  be  an  almost  equal 
demand  at  all  times  on  the  positive  and 
negative  main,  and  the  current  which  flows 
in  the  third  or  middle  wire  will  be  very  small. 
This  is  the  principle  of  the  "  three-wire 
system  "  of  distribution  of  electricity  invented 
simultaneously  by  Mr.  Edison  and  the  late 
Dr.  Hopkinson.  It  is  now  the  system 
generally  used  in  public  electricity  supply. 
The  middle  wire  has  to  be  connected  to 
corresponding  feeders  and  thus  brought  back 
to  the  central  station,  where  some  apparatus 
for  the  division  of  the  voltage  between  the 
outer  wires  must  be  provided.  In  stations 


238  ELECTRICITY 

using  a  secondary  battery  the  division  of  the 
voltage  can.  easily  be  made  by  bringing  the 
middle  wire  to  the  centre  of  the  battery;  or 
a  so-called  "  balancing  set "  may  be  provided, 
consisting  of  two  dynamos  coupled  in  series 
and  connected  across  the  outer  wires.  These 
are  small  idle-running  machines  whose  sole 
office  is  to  divide  the  total  voltage  into  two 
equal  components.  The  middle  wire  is 
attached  to  the  connection  between  the  two 
dynamos.  These  dynamos  may*  be  quite 
small,  since  the  out- of -balance  current  brought 
to  them  by  the  middle  wire  is  only  a  very 
small  fraction  of  the  total  current  supplied 
to  the  outer  wires;  generally  only  a  few  per 
cent.  It  suffices,  therefore,  to  give  the  middle 
wire  about  half  the  cross  section  of  one  of  the 
outer  wires,  both  in  the  feeders  and  in  the 
distributing  mains.  By  using  the  three- 
wire  system  the  total  amount  of  copper 
required  for  the  supply  of  electricity  through- 
out a  given  district  is  thus  reduced  to  about 
32  per  cent,  of  the  amount  that  would  be 
required  for  the  same  service  at  the  same 
lamp  voltage  with  a  two-wire  system. 

This  relation  holds  good  whether  the  supply 
is  that  of  a  continuous  or  that  of  an  alternating 
current.  In  the  latter  case  there  is  sometimes 


DISTRIBUTION  OF  ELECTRICITY    239 

a  further  possibility  for  economy  in  copper 
by  the  use  of  balancing  transformers.  In  the 
orthodox  method  of  working  the  three-wire 
system  the  feeders  as  well  as  the  mains  are 
provided  with  the  third  wire.  It  is  necessary 
to  carry  the  third  feeder  wire  back  to  the 
central  station,  because  it  is  at  the  central 
station  where  the  division  of  voltage  into  the 
positive  and  negative  part  of  the  system  is 
made.  With  continuous  current  this  is  neces- 
sarily so,  because  the  subdivision  of  the  voltage 
requires  either  a  storage  battery  or  machinery 
in  motion.  If  the  supply  is  by  alternating 
current,  then  the  subdivision  of  voltage  can 
be  made  by  an  apparatus  which  is  not  in 
motion  and  requires  no  supervision.  This 
apparatus  need,  therefore,  not  be  placed  in 
the  central  station  where  the  feeder  starts, 
but  at  the  feeding  point  or  near  it  on  the  mains 
where  the  feeder  ends.  The  third  wires  need 
then  only  be  provided  for  the  mains,  but  may 
be  omitted  from  the  feeders.  The  apparatus 
for  the  subdivision  of  the  voltage  between 
the  two  outer  wires  of  the  main  is  simply  a 
transformer  with  an  equal  number  of  turns 
in  its  primary  and  secondary  coil.  Both 
coils  must  in  reality  be  considered  as  the  two 
halves  of  one  single  coil ;  the  middle  point  is 


240  ELECTRICITY 

connected  to  the  third  wire,  whilst  the  ter- 
minals are  attached  to  the  two  outside  wires. 
Such  a  transformer  is  technically  termed  an 
"  auto-transformer,"  and  where  the  ratio  of 
the  windings  is  as  1  to  1,  it  simply  serves  to 
halve  the  total  voltage  and  allow  whatever 
out  of  balance  current  may  flow  in  the  middle 
wire  to  find  its  way  back  to  the  outer  wires. 

By  the  means  here  described  it  is  possible 
to  give  a  satisfactory  service  of  electricity 
over  a  district  extending  for  about  a  mile  all 
round  the  central  station.  The  term  "  central 
station  "  is  derived  from  the  fact  that  in  the 
early  days  of  the  public  supply  of  electricity 
the  works  where  the  current  was  generated 
were  placed  as  near  the  centre  of  the  district 
of  supply  as  was  found  possible.  Now-a-days 
it  is  not  a  correct  term.  The  tendency  is 
to  put  the  works  eccentrically  to  the  supply 
area;  and  this  for  obvious  reasons.  In  the 
central  part  of  the  town,  where  there  is  the 
greatest  demand  for  current,  land  is  too 
valuable  to  be  occupied  by  a  works,  there  is 
the  difficulty  of  bringing  coal  to  the  works, 
taking  the  ashes  away,  and  there  is  the  further 
difficulty  of  obtaining  an  abundant  water 
supply  for  condensing  purposes.  It  is  true 
that  if  the  water  supply  is  restricted  cooling 


DISTRIBUTION  OF  ELECTRICITY    241 

towers  may  be  used,  but  then  there  is  the 
probability  that  these,  by  giving  off  steam, 
will  prove  a  public  nuisance.  The  noise  and 
vibration  inseparable  from  the  use  of  powerful 
machinery  have  also  to  be  taken  into  con- 
sideration, so  that  on  the  whole  a  central 
position  for  the  electricity  works  becomes 
impossible.  If  we  still  speak  of  a  central 
station,  the  term  must  not  be  used  in  a 
topographical  sense,  but  rather  as  indicating 
that  in  those  works  the  generation  of  elec- 
tricity required  over  an  extended  area  has 
been  centralised. 

But  if  we  place  the  station  outside  the 
boundary  of  the  town  it  is  no  longer  com- 
mercially possible  to  supply  the  district  with 
current  at  the  moderate  pressure  of  440  or 
500  volts.  The  feeders  are  necessarily  long 
and  their  resistance  is  high.  To  get  an  efficient 
transmission  system  we  must  raise  the  pressure 
to  a  very  much  higher  value,  far  above  that 
which  is  suitable  for  the  lamps.  This  leads 
to  the  establishment  of  so-called  "  sub- 
stations "  within  the  supply  area.  These 
sub-stations  receive  high-pressure  current 
from  the  central  station  outside  of  the  town, 
and  convert  it  to  such  a  pressure  as  renders 
the  current  directly  applicable.  Thus  the 
Q 


242  ELECTRICITY 

sub-stations  become  topographically  central 
stations  for  a  limited  area.  The  objections 
to  central  stations  mentioned  above  do  not 
apply  to  sub-stations.  They  use  neither 
coal  nor  water,  they  need  not  necessarily 
contain  moving  machinery,  and  if  such 
machinery  is  erected  in  a  sub-station  it  is  of 
purely  rotative  type,  such  as  electric  motors 
and  generators,  which  work  without  causing 
any  noise  or  vibration ;  and  finally  the  amount 
of  space  required  is  very  small,  so  that  the 
cost  of  land,  even  in  the  middle  of  the  town, 
is  no  longer  prohibitive.  Where  the  supply 
is  by  alternating  current  no  land  at  all  is 
required.  The  converting  apparatus  consists 
mainly  of  transformers  which  may  be  put 
either  under  the  pavement  or  in  kiosks  at 
street  corners. 

If  a  continuous  current  supply  must  be 
given  to  the  householders,  then  there  must  be 
in  the  sub-station  not  only  a  conversion  as  to 
voltage,  but  also  as  to  type  of  current.  The 
conveyance  of  electric  power  from  the  central 
station  to  the  sub-station  is  done  most 
economically  by  means  of  three-phase  current. 
This  current  is  used  to  drive  machinery  which 
produces  continuous  current.  Such  an 
arrangement  is  shown  diagrammatically  in 


DISTRIBUTION  OF  ELECTRICITY    243 

Fig.  25.  M  is  a  three-phase  motor  driven  by 
the  high-pressure  current  coming  from  the 
central  station.  G  is  an  ordinary  D.C. 
generator  directly  coupled  to  the  motor. 
The  sub -station  may  be  provided  with  a 
number  of  such  units,  storage  batteries  may 
be  used,  and  the  whole  service  is  carried  on 
exactly  as  in  a  D.C.  central  station,  the  only 


FIG.  25. 

difference  being  that  there  are  no  boilers, 
engines,  chimney,  condensing  plant,  coal 
bunkers  or  ashpit,  and  no  danger  of  the 
works  becoming  a  nuisance  to  the  neighbour- 
hood. All  the  plant  which  in  the  main 
station  is  required  for  the  generation  of  power 
is  here  represented  by  electric  motors.  The 
space  occupied  is  quite  small  and  the  service 
exceedingly  simple.  In  so  far  as  simplicity 
of  operation  goes  the  system  is  admirable; 


244  ELECTRICITY 

it  has,  however,  some  minor  defects.  The 
whole  of  the  power  has  to  undergo  a  double 
conversion.  In  the  central  station  the 
mechanical  power  of  the  steam  engines  must 
be  converted  into  the  electrical  power  re- 
presented by  the  three-phase  high-pressure 
current;  this  at  the  sub-station  has  again 
to  be  converted  into  mechanical  power  by 
means  of  the  electric  motors,  and,  finally, 
this  mechanical  power  must  be  again  re- 
converted into  the  electric  power  of  the  low- 
pressure  continuous  current  which  is  supplied 
to  the  users  of  electricity.  This  chain  of 
repeated  conversions  lowers  the  efficiency. 
At  full  load  the  efficiency  of  a  motor  generator 
set  as  represented  by  Fig.  25  scarcely  exceeds 
83  per  cent.  It  should  further  be  noted  that 
for  every  kw.  capacity  in  the  D.C.  side  of 
the  set,  about  1*2  kw.  capacity  must  be 
provided  in  the  A.C.  side,  so  that  the  total 
dynamo  capacity  in  the  sub-station  must 
be  more  than  twice  the  output  capacity. 
This  makes  the  system  expensive  in  capital 
outlay,  whilst  the  low  efficiency  makes  it 
expensive  in  working. 

Both  these  defects  are  to  a  large  extent 
overcome  by  the  use  of  so-called  "  rotary 
converters,"  illustrated  diagrammatically  in 


DISTRIBUTION  OF  ELECTRICITY    245 


Fig.  26.  Here,  instead  of  using  two  distinct 
machines,  namely  a  motor  and  a  generator, 
only  one  machine  is  used,  which  fulfils  both 
functions  at  once.  This  machine,  moreover, 
is  smaller  than  either  M  or  G  of  Fig.  25, 
so  that  the  capital  outlay  is  considerably 
reduced.  The  converter  C  is  an  ordinary 
D.C.  machine  with  the  addition  of  suitable 


FIG.  26. 

connections  by  which  alternating  current 
can  be  supplied  to  the  same  armature  from 
which  the  continuous  current  is  taken.  The 
wires  on  the  armature  are  thus  simultaneously 
traversed  by  the  alternating  current  which 
drives  the  machine  and  by  the  continuous 
current  which  is  generated  in  the  machine  by 
reason  of  its  being  driven.  Without  going 
minutely  into  the  somewhat  complicated 
theory  of  the  action  of  this  type  of  machine, 
it  will  be  clear  that  by  Lenz's  law  the  direction 


246  ELECTRICITY 

of  the  current  which  produces  motion  must  on 
the  whole  be  opposed  to  the  direction  of  the 
current  produced  by  this  motion.  Thus  in 
each  armature  wire  the  A.C.  and  D.C.  flowing 
simultaneously  neutralise  each  other  to  some 
extent.  This  neutralisation  can  obviously 
not  be  absolute,  for  one  current  is  alternating, 
that  is  continually  changing,  and  the  other  is 
continuous,  that  is  of  constant  value.  At 
times  the  one  and  at  other  times  the  other 
current  predominates,  but  on  the  whole  the 
difference  between  the  two  currents  is  smaller 
than  either,  and  that  is  the  reason  why  a 
given  D.C.  machine,  if  used  as  a  converter, 
will  give  on  its  D.C.  side  nearly  twice  the  out- 
put that  can  be  taken  from  the  same  machine 
if  worked  as  an  ordinary  D.C.  generator. 

The  connections  for  the  supply  of  the  A.C. 
are  tappings  of  the  armature  winding  brought 
out  to  so-called  "  slip  rings  "  S  on  which 
brushes  bear.  Since  the  same  armature 
winding  serves  both  the  A.C.  and  the  D.C. 
side  of  the  machine,  and  since  the  e.m.f. 
induced  in  both  is  produced  by  the  wires  of 
the  armature  cutting  through  the  same 
magnetic  flux,  it  will  be  obvious  that  there 
must  be  a  definite  relation  between  the  e.m.f. 
of  the  alternating  and  that  of  the  continuous 


DISTRIBUTION  OF  ELECTRICITY    247 

current.  The  ratio  between  the  two  e.m.f.'s 
varies  a  little  with  the  constructive  details, 
but  may  be  taken  as  about  2  to  3,  so  that  if 
500  volts  is  required  at  the  D.C.  side,  an 
A.C.  of  about  330  volts  must  be  supplied  to 
the  slip  rings.  Obviously  this  is  far  too  low 
a  pressure  for  economic  transmission  of 
electric  power  from  the  central  station.  To 
carry  the  thousands  of  kw.  required  for  the 
supply  of  a  town  from  the  central  station  to 
the  sub-stations  by  means  of  cables  of 
moderate  size  and  cost,  we  require  pressures 
of  10,000  volts  or  more,  so  that  the  use  of 
a  transformer,  T,  becomes  necessary.  The 
use  of  this  transformer  has  the  incidental 
advantage  that  we  obtain  an  easy  and  in- 
expensive way  of  subdividing  the  pressure 
between  the  outer  wire  if  the  distribution 
on  the  D.C.  side  is  to  be  made  on  the  three- 
wire  system.  We  need  only  attach  the  zero, 
or. middle  wire  o,  to  the  electrical  centre  of  the 
secondary  winding  of  the  transformer  as 
shown. 

The  efficiency  of  a  converter  set,  including 
the  transformer,  is  sensibly  higher  than  that 
of  a  motor  generator  set.  It  generally 
reaches  92  per  cent.  In  another  respect  the 
converter  has  also  an  advantage  over  the 


248  ELECTRICITY 

motor  generator.  Since  the  motor  is  of  the 
non-synchronous  type,  its  power  factor  must 
be  less  than  unity.  This  means  that  the 
feeder  coming  from  the  central  station  has  to 
carry  rather  more  current  than  corresponds 
to  the  actual  energy  transmitted.  This  extra 
amount  of  current  brings  no  power;  it  only 
heats  the  feeder  and  lowers  the  efficiency  of 
transmission.  It  also  makes  it  necessary 
to  make  the  A.C.  generators  at  the  central 
station  rather  larger  than  would  be  the  case 
if  these  machines  were  called  upon  to  give 
only  the  useful  component  of  the  current. 
A  power  factor  less  than  unity  at  the  delivery 
end  of  the  feeders  means,  therefore,  not  only 
stouter  and  more  expensive  cables,  but  also 
somewhat  more  expensive  plant  at  the  central 
station.  This  drawback  of  the  motor  generator 
does  not  obtain  in  sub-stations  where  con- 
verters are  used.  The  converter,  as  far  as 
the  A.C.  side  is  concerned,  is  a  synchronous 
motor,  and  in  such  a  machine  it  is  always 
possible  to  so  adjust  the  excitation  that  the 
armature  will  take  the  A.C.  exactly  co-phasal 
with  the  alternating  e.m.f.  It  is  thus  always 
possible  to  work  with  a  power  factor  equal  to 
unity,  and  the  current  delivered  by  the 
generators  at  the  central  station  has 'no  idle, 


DISTRIBUTION  OF  ELECTRICITY    249 

or  so-called  "  wattless "  component.  Its 
absolute  value  is  therefore  exactly  commen- 
surate with  the  power  it  actually  transmits. 
The  cables  need  not  be  stouter  than  corre- 
sponds to  the  power  they  actually  deliver, 
and  the  generators  need  not  be  made  larger 
than  corresponds  to  the  actual  power  devel- 
oped by  their  engines.  Since  a  rotary  con- 
verter is  a  synchronous  machine,  it  must  be 
first  run  up  to  speed  before  being  switched 
on  to  the  A.C.  side.  This  may  be  done  by  a 
small  non-synchronous  starting  motor  mounted 
on  the  shaft  of  the  converter,  or,  if  batteries 
are  used  at  the  sub-station,  the  converter 
may  be  run  up  to  speed  by  D.C.  derived 
from  the  batteries. 

A  very  important  application  of  rotary 
converters  is  in  connection  with  electric 
tramways  and  railways  working  with  con- 
tinuous current.  The  working  D.C.  voltage 
of  tramways  is  about  500  V.,  that  of  railways 
is  generally  a  little  higher:  in  Europe  600 
to  750,  and  in  some  cases  1000  V.  In  America 
some  lines  are  worked  at  1200  V.,  and  one 
in  England  is  now  being  equipped  for  3500 
volts;  but  even  at  this  pressure,  the  direct 
supply  of  D.C.  from  the  generating  station 
to  the  trolley  wire  would  require  so  great  an 


250  ELECTRICITY 

A 

expenditure  of  copper  for  feeders  as  to  make 
the  system  commercially  impossible  on  any  but 
fairly  short  lines.  It  thus  becomes  necessary 
to  transmit  electricity  from  the  power-house 
at  high  pressure  to  sub-stations  placed  at 
intervals  along  the  line,  and  to  convert  the 
three-phase  high-pressure  current  at  these 
sub-stations  into  continuous  current,  which  is 
supplied  by  means  of  feeders  to  the  trolley 
line.  The  apparatus  used  is  of  the  type 
shown  in  Fig.  26,  with  this  difference,  that  the 
middle  wire  o  on  the  D.C.  side  is  omitted  and 
that  the  negative  brush  is  connected  to  the 
rails  or  by  way  of  a  switch-board  to  the 
negative  return  feeders  bringing  the  current 
back  from  the  rails,  whilst  the  positive  brush 
is  connected  with  an  omnibus  bar  on  the 
main  switch-board  from  which  all  the  feeders 
start. 

The  current  taken  by  electric  tramways 
and  railways  is  very  fluctuating.  In  the 
case  of  tramways  the  fluctuations  are  the  less 
felt  the  larger  the  system,  that  is  to  say,  the 
greater  the  number  of  cars  drawing  current 
from  a  particular  power-house  or  sub-station. 
If  only  a  small  number  of  cars  is  on  the  system 
the  fluctuations  may  become  very  great. 
This  is  especially  the  case  if  a  block  in  the 


DISTRIBUTION  OF  ELECTRICITY    251 

traffic  occurs,  and  on  the  street  being  freed 
from  the  block  all  the  cars  in  that  street  start 
at  once.  In  electric  railways  the  fluctuations 
are  even  greater  than  on  tramways,  because 
there  are  not  so  many  motors  simultaneously 
in  use  whose  demand  for  current  may,  as  in 
very  large  tramway  systems,  more  or  less 
average  out  to  a  fairly  steady  load.  The 
generators  in  a  traction  station  are  thus 
subjected  to  great  and  quick  changes  of  load. 
To  mitigate  the  excessive  stresses  brought  on 
to  the  generating  plant  by  these  violent 
fluctuations  of  load,  storage  batteries  may  be 
used  which  act  as  a  kind  of  reservoir  of  energy, 
taking  in  a  charging  current  at  the  times  that 
the  line  requires  less  than  a  certain  amount  of 
current,  and  giving  a  discharge  current  and 
thus  helping  the  engines  at  the  time  that  the 
demand  for  current  on  the  line  becomes 
excessive.  The  storage  battery  acts  as  a  sort 
of  elastic  buffer  between  the  power-house  and 
the  trains,  and  it  is  therefore  called  a  "  buffer 
battery."  The  buffer  battery  may  be  used 
either  in  the  main  power-house  or  in  the  sub- 
station ;  in  either  case  its  advantages  are  that 
the  generating  machinery  may  be  reduced  in 
size.  It  has  not  to  be  large  enough  for  the 
occasional  and  excessive  demand,  but  only 


252  ELECTRICITY 

a  little  larger  than  corresponds  to  the  average 
demand.  There  is  the  further  advantage 
that  the  engines  are  worked  at  a  steady 
load,  and  therefore  with  a  maximum  of 
efficiency. 


BIBLIOGRAPHY 

HANDBOOKS  FOR  BEGINNERS 

Technical  Electricity,  by  DAVIDGE  and  HUTCHINSON  (University 
Tutorial  Press). 

Magnetism  and  Electricity  for  Beginners,  by  H.  E.  HADLEY 
(Macmillan). 

Elementary  Lessons  in  Electricity  and  Magnetism,  by  S.  P. 
THOMPSON  (Macmillan). 

The  Electromagnet,  by  S.  P.  THOMPSON  (Spon). 

Practical  Electricity  and  Magnetism,  by  J.  HENDERSON  (Long- 
mans). 

THEORETICAL  WORKS  FOR  ADVANCED  STUDENTS 

Absolute  Measurements  in  Electricity  and  Magnetism,  by  A. 

GRAY  (Macmillan). 
Elementary  Treatise  on  Electricity  and  Magnetism,  by  FOSTER 

and  PORTER  (Longmans). 
Elements  of  Electricity  and  Magnetism,  by  Sir  J.  THOMSON 

(Cambridge  University  Press). 

Modern  Views  of  Electricity,  by  Sir  OLIVER  LODGE  (Macmillan). 
The    Propagation    of  Electric    Currents,   by  J.    A.    FLEMING 

(Constable). 

BOOKS  ON  ELECTRICAL  ENGINEERING  FOR  ADVANCED 

STUDENTS 

Dynamo  Electric  Machinery,  by  S.  P.  THOMPSON  (Spon). 
The  Dynamo,  by  HAWKINS  and  WALLIS  (Whittaker). 
Transformers,  by  KAPP  (Whittaker). 
Electrical  Engineering,  by  THOMAELEN,  translated  by  G.  W; 

HOWE  (Arnold). 

Electrical  Engineering,  by  H.  SIMMONS  (Cassell). 
Experimental  Electrical  Engineering,  by  KARAPETOFF  (Wiley). 
Power  House  Design,  by  SNELL  (Longmans). 
Electric  Traction,  by  WILSON  and  LYALL  (Arnold). 
Telegraphy,  by  T.  E.  HERBERT  (Whittaker). 
Principles  of  Wireless  Telegraphy,  by  G.  W.  PlEECE  (McGraw 

Hill  Book  Company). 


INDEX 


ACCUMULATOR,  54 
Alternating  current,  180 
Alternator,  186 
Amperemeter,  156 
Ampere's  rule,  145 
Ampere,  the  technical  unit  of  cur- 
rent, 150 

Ampere  turns,  152 
Auto-transformer,  240 

Balancing  set,  238 
Ballast  resistance,  138 
Biot-Savart's  law,  149 
Boosting  dynamo,  234 
Brushes,  178 
Buffer  battery,  251 

Capacity,  75 

Central  station,  240 

C.G.S.  system,  19 

Characteristic   of    magnetisation, 

169 

Commutator,  189 
Compound  machine,  202 
Condenser,  78 
Conductivity,  129 
Contact  E.M.F.,  table  of,  47 
Core  transformer,  216 
Coulomb's  balance,  57 

Drum  winding,  194 
Dyne,  19 

Effective    value   of   current    and 

voltage,  209 

Electro-chemical  equivalents,  125 
Electrolysis,  119 
Electromagnetic  system,  32 
Electromotive  force,  42 
Electrostatic  system,  26 
Erg,  the  c.g.s.  unit  of  energy,  172 

Faraday  cage,  85 
Feeders,  230 
Ferraris'  discovery,  218 
Force  between  electric  charges,  25 
„    between  magnetic  masses,  31 


Force,  definition  of,  16 

,,      of  mass  attraction,  19 

,,      unit  of,  in  c.g.s.  system,  19 

Frequency,  180,  206 

Fuses,  128 

Galvanism,  37 
Gramme  winding,  191 

Heat  developed  by  current,  126 
Horse-power,  the  engineer's  unit  of 
power,  173 

Influence  machines,  97,  106 

Joule,  the  practical  unit  of  energy, 
173 

Kilowatt,  the   engineer's  unit  of 
power,  172 

Lena's  law,  50,  171 

Magnetic  force,  161 

„         induction,  146 
,,         moment,  29 
,,         permeability,  31 

Mains,  230 

Mirror  galvanometer,  155 

Oersted's  experiment,  144 
Ohm's  law,  131 

Pacinotti's  machine,  189 
Potential,  44,  55,  63 
Power,  171 

„      factor,  214 
Pyrometer,  135 

Replenisher,  103 
Residual  charge,  115 

„        magnetism,  200 
Resistance,  specific,  132 
Ring  winding,  191 
Rotary  converter,  244 
Rotor,  184,  222 

Self-excitation,  200 


255 


256 


INDEX 


Scries  machine,  200 

Shell  transformer,  217 

Shunt  machine,  201 

Slip,  227 

Solenoid,  143 

Specific   inductive    capacity,    27, 

81 
Speed  of  light,  32 

,,  of  meteorite,  69 
Squirrel  cage  rotor,  225 
Standard  frequency  for  railways, 

207 

Stator,  183,  223 
Sub-station,  241 
Synchronous  motor,  218 
Syphon  recorder,  102 


Tangent  galvanometer,  153,  166 
Temperature  coefficient,  136 
Three-phase  machine,  187 
Three-wire  system,  237 
Transformer,  215 

Unit  of  current  strength,  150 
,,    of  electric  charge,  ^26 
„    of  magnetic  matter,  32,  146 

Vector,  209 

Volta's  discovery  of  contact  elec- 
tricity, 38 

Volt,  the  practical  unit  of  e.rn.f., 
178 

Water-dropping  machine,  98 


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22.  The  Papacy  and  Modern  Times. 

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astic, so  clear  and  witty,  and  so  well  adapted  to  the  general  reader." 
— American  Library  Association  Booklist. 

17.  Crime  and  Insanity. 

By  DR.  C.  A.  MERCIER,  author  of  Text-Book  of  Insanity,  etc. 

12.  The  Animal  World. 

By  PROF.  F.  W.  GAMBLE. 

15.  Introduction  to  Mathematics. 

By  A.  N.  WHITEHEAD,  author  of  Universal  Algebra. 

PHILOSOPHY  AND  RELIGION 

69.  A  History  of  Freedom  of  Thought. 

By  JOHN  B.  BURY,  M.  A.,  LL.  D.,  Regius  Professor  of  Modern  His- 
tory in  Cambridge  University.  Summarizes  the  history  of  the  long 
struggle  between  authority  and  reason  and  of  the  emergence  of  the 
principle  that  coercion  of  opinion  is  a  mistake. 

55.  Missions :  The^'r  Rise  and  Development. 

By  MRS.  MANDELL  CREIGHTON,  author  of  History  of  England.  The 
author  seeks  to  prove  that  missions  have  done  more  to  civilize  the 
world  than  any  other  human  agency. 

52.  Ethics. 

By  G.  E.  MOORE,  Lecturer  in  Moral  Science,  Cambridge.  Discusses 
what  is  right  and  what  is  wrong,  and  the  whys  and  wherefores. 

65.  The  Literature  of  the  Old  Testament. 

By  GEORGE  F.  MOORE,  Professor  of  the  History  of  Religion,  Harvard 
University.  "A  popular  work  of  the  highest  order.  Will  be  profit- 
able to  anybody  who  cares  en9ugh  about  Bible  study  to  read  a  serious 
book  on  the  subject." — American  Journal  of  Theology, 

50.  The  Making  of  the  New  Testament. 

By  B.  W.  BACON,  Professor  of  New  Testament  Criticism,  Yale.  An 
authoritative  summary  of  the  results  of  modern  critical  research 
with  regard  to  the  origins  of  the  New  Testament. 


35.  The  Problems  of  Philosophy. 

By  BERTRAND  RUSSELL,  Lecturer  and  Late  Fellow,  Trinity  College, 
Cambridge. 

44.  Buddhism. 

By  MRS.  RHYS  DAVIDS,  Lecturer  on  Indian  Philosophy,  Manchester. 

46.  English  Sects:  A  History  of  Nonconformity. 

By  W.  B.  SELBIE,  Principal  of  Manchester  College,  Oxford. 

60.  Comparative  Religion. 

By  PROF.  J.  ESTLIN  CARPENTER.  "One  of  the  few  authorities  on  this 
subject  compares  all  the  religions  to  see  what  they  have  to  offer  on 
the  great  themes  of  religion." — Christian  Work  and  Evangelist. 

88.  Religious  Development  Between  Old  and  New 
Testaments. 

By  R.  H.  CHARLES,  Canon  of  Westminster.  Shows  how  religious 
and  ethical  thought  betwee .-t  180  B.  C.  and  100  A.  D.  grew  naturally 
into  that  of  the  New  Testament. 

LITERATURE  AND  ART 

73.  Euripides  and  His  Age. 

By  GILBERT  MURRAY,  Regius  Professor  of  Greek,  Oxford.  Brings 
before  the  reader  an  undisputedly  great  poet  and  thinker,  an  amaz- 
ingly successful  playwright,  and  a  figure  of  high  significance  in  the 
history  of  humanity. 

81.  Chaucer  and  His  Times. 

By  GRACE  E.  HADOW,  Lecturer  Lady  Margaret  Hall,  Oxford;  Late 
Reader,  Bryn  Mawr. 

70.  Ancient  Art  and  Ritual. 

By  JANE  E.  HARRISON,  LL.  D.,  D.  Litt.  "One  of  the  100  most  im- 
portant books  of  1913." — New  York  Times  Review. 

61.  The  Victorian  Age  in  Literature. 

By  G.  K.  CHESTERTON.  The  most  powerfully  sustained  and  brilliant 
piece  of  writing  Mr.  Chesterton  has  yet  published. 

59.  Dr.  Johnson  and  His  Circle. 

By  JOHN  BAILEY.  Johnson's  life,  character,  works,  and  friendships 
are  surveyed;  and  there  is  a  notable  vindication  of  the  "Genius  of 

Boswell." 

58.  The  Newspaper. 

By  G.  BINNEY  DIBBLE.  The  first  full  account,  from  the  inside,  of 
newspaper  organization  as  it  exists  to-day. 

62.  Painters  and  Painting. 

By  SIR  FREDERICK  WEDMORE.     With  16  half-tone  illustrations. 

64.  The  Literature  of  Germany. 

By  J.  G.  ROBERTSON. 

48.  Great  Writers  of  America. 

By  W.  P.  TRENT  and  JOHN  ERSKINE,  of  Columbia  University. 

87.  The  Renaissance. 

By  EDITH  SICHEL,  author  of  Catherine  de  Medici,  Men  and  Women 
of  the  French  Renaissance. 


93.  An  Outline  of  Russian  Literature. 

By  MAURICE  BARING,  author  of  The  Russian  People,  etc.  Tols- 
toi, Tourgenieff,  Dostoieffsky,  Pushkin  (the  father  of  Russian 
Literature),  Saltykov  (the  satirist),  Leskov,  and  many  other  authors. 

40.  The  English  Language. 

By  L.  P.  SMITH.     A  concise  history  of  its  origin  and  development. 

45.  Medieval  English  Literature 

By  W.  P.  KER,  Professor  of  English  Literature,  University  Col- 
lege, London.  "One  of  the  soundest  scholars.  His  style  is  effec- 
tive, simple,  yet  never  dry." — The  Athenaeum. 

89.  Elizabethan  Literature. 

By  J.  M.  ROBERTSON,  M.  P.,  author  of  Montaigne  and  Shake- 
speare, Modern  Humanists. 

27.  Modern  English  Literature. 

By  G.  H.  MAIR.  From  Wyatt  and  Surrey  to  Synge  and  Yeats. 
"One  of  the  best  of  this  great  series." — Chicago  Evening  Post. 

2.  Shakespeare. 

By  JOHN  MASEFIELD.  "One  of  the  very  few  indispensable  ad- 
juncts to  a  Shakespearean  Library." — Boston  Transcript. 

31.  Landmarks  in  French  Literature. 

By  G.  L.  STRACHEY,  Scholar  of  Trinity  College,  Cambridge.  "It 
is  difficult  to  imagine  how  a  better  account  of  French  Literature 
could  be  given  in  250  pages." — London  Times. 

38.  Architecture. 

By  PROF.  W.  R.  LETHABY.  An  introduction  to  the  history  and 
theory  of  the  art  of  building. 

66.  Writing  English  Prose. 

By  WILLIAM  T.  BREWSTER,  Professor  of  English,  Columbia  Univer- 
sity. "Should  be  put  into  the  hands  of  every  man  who  is  begin- 
ning to  write  and  of  every  teacher  of  English  that  has  brains 
enough  to  understand  sense." — New  York  Sun. 

83.  William  Morris:  His  Work  and  Influence. 

By  A.  GLUTTON  BROCK,  author  of  Shelley:  The  Man  and  the  Poet. 
William  Morris  believed  that  the  artist  should  toil  for  love  of  his 
work  rather  than  the  gain  of  his  employer,  and  so  he  turned 
from  making  works  of  art  to  remaking  society. 

75.  Shelley,  Godwin  and  Their  Circle. 

By  H.  N.  BRAILSFORD.  The  influence  of  the  French  Revolution 
on  England. 

OTHER     VOLUMES    IN    PREPARATION. 

HENRY  HOLT  AND  COMPANY 
34  West  33d  Street  New  York 


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